Precision fabrication of diverse polymer microstructures by use of the hydrophobic effect, including microlens arrays, microlenses self-aligned to optical fibers, conductive bump bonds self-aligned to bump pads, and bonds between mutually perpendicular substrates

ABSTRACT

High performance microlens arrays are fabricated by (i) depositing liquid on the hydrophilic domains of substrates of patterned wettability by either (a) condensing liquid on the domains or (b) withdrawing the substrate from a liquid solution and (ii) optionally curing the liquid to form solid microlenses. The f-number (f # ) of formed microlenses is controlled by adjusting liquid viscosity, surface tension, density, and index of refraction, as well as the surface free energies of the hydrophobic and hydrophilic areas. The f-number of formed microlenses is also adjustable by controlling substrate dipping angle and withdrawal speed, the array fill factor and the number of dip coats used. At an optimum withdrawal speed f #  is minimized and array uniformity is maximized. At this optimum, arrays of f/3.48 microlenses were fabricated using one dip-coat with uniformity better than Δf/f˜±3.8% while multiple dip-coats permit production of f/1.38 microlens arrays and uniformity better than Δf/f˜±5.9%. Average f # s are reproducible to within 3.5%. The method is adaptable and extendible to precision parallel fabrication of (i) microlenses precisely sized, aligned and spatially positioned to various small light sources and optical fiber ends, (ii) conductive bump bonds on substrate pads, and (iii) conductive bonds between corresponding domains on separate perpendicular substrates, all of which are self-aligned.

RELATION TO A PROVISIONAL PATENT APPLICATION

[0001] The present patent application is descended from, and claimsbenefit of priority of, U.S. provisional patent application Serial No.60/184,605 filed on Feb. 24, 2000, for LOW COST, ACCURATE PATTERNING OFHYDROPHOBIC MATERIALS TO ALLOW THE ASSEMBLY OF ORGANIC AND INORGANICCOMPONENTS ON A SUBSTRATE to the selfsame inventors as the presentpatent application.

[0002] This invention was made by support of the U.S. Government underGrant No. DARPA-HOTC MDA 972-98-1-0001 (Defense Advanced ResearchProject Agency—Heterogeneous Optoelectronic Technology Center) actingthrough the United States Defense Advanced Research Project Agency(DARPA). The U.S. Government has certain rights in this invention.

BACKGROUND OF THE INVENTION

[0003] 1. Field of the Invention

[0004] The present invention generally concerns (i) microstructuresincluding optical microlenses and electrical bump bonds; (ii) liquids(and especially liquid monomers that may be cured to form polymers) andthe use of such liquids in the fabrication of microstructures; and (iii)the use of hydrophobic and hydrophilic effects in the fabrication ofmicrostructures, including optical microlenses, electrical bump bonds,and electrical bonds between mutually perpendicular chips.

[0005] The present invention particularly concerns the precisionfabrication of, inter alia, (i) high performance transparent polymeroptical microlenses and microlens arrays, including as may be eitherarrayed or aligned, including self-aligned, to the ends of opticalfibers, and, separately by an analogous process, (ii) electricallyconductive polymer bump bonds, and conductive bump bonds self-aligned tobump pads, and, separately by an analogous process, (iii) bonds betweenmutually perpendicular substrates.

[0006] In all areas (i)-(iii) the present invention still moreparticularly concerns microlens or bump bond or substrate(s) bondfabrication by (1) transfer of a liquid polymer precursor ontohydrophilic domains of a substrate of patterned wettability followed by(2) curing of the polymer; said (1) transfer of liquid being realizedeither by (1a) condensing the liquid onto these hydrophilic domains or(1b) withdrawing substrates of patterned wettability from a liquidsolution at controlled speed and said (2) curing being realized by (2a)heat, (2b) chemical reaction or (2c) ultraviolet light.

[0007] In area (i) the present invention still more particularlyconcerns aligning microlenses to optical components, and the directfabrication of microlenses on optical components.

[0008] Also in the area (i) the present invention still moreparticularly concerns the low cost fabrication of microlenses that areself-aligned to optical fibers and/or low-wavelength (<500 nm)single-mode light output devices, including microlenses as may befabricated both (i) directly upon these fibers or components or (ii) ina precisely spaced and oriented relationship thereto.

[0009] In the area (ii), the electrically conductive polymer bumpbonds—the fabrication of which is an area of the present invention—maystill more particularly be (i) arrayed and/or (ii) self-aligned, by theuse of hydrophobic and hydrophilic effects.

[0010] Likewise in the area (iii), the electrically conductive bondsbetween perpendicular substrates—the fabrication of which is anotherarea of the present invention—may still more particularly be (i) arrayedand/or (ii) self-aligned, to either or to both substrates by the use ofhydrophobic and hydrophilic effects.

[0011] 2. Description of the Prior Art

[0012] 2.1 Microlenses

[0013] In today's world (circa 2001) of information processing, the roleof arrayed optics is becoming more and more important as the need forparallelism and density increases in each of display, communication, andstorage applications. The trend towards highly parallel compact opticalsystems has in particular lead to a growing need for high-performance,low f-number (f^(#)), microlens arrays.

[0014] Refractive microlenses have been utilized in hybrid opticalinterconnect strategies. See, for example, M. R. Taghizadeh“Micro-optical fabrication technologies for optical interconnectionapplications”, in Diffractive Optics and Micro-Optics, OSA TechnicalDigest, 260 (2000); M. W. Haney “Micro- vs. macro-optics in free-spaceoptical interconnects” in Diffractive Optics and Micro-Optics, OSATechnical Digest, 266 (2000) ; S. Eitel, S. J. Fancey, H. P. Gauggel, K.H. Gulden, W. Bachtold, M. R. Taghizadeh, “Highly uniformvertical-cavity surface-emitting lasers integrated with microlensarrays”, IEEE Photonics Technology Letters 12, IEEE,. 459-61 (2000); andG. Sharp, L. E. Schmutz, “Microlens arrays meet any challenge”, Lasers &Optronics Lasers Optronics (USA) 16, 21-3 (1997).

[0015] Refractive microlenses have also been used in switching networks.See, for example, M. C. Wu, L. Y. Lin, S. S. Lee, C. R. King,“Free-space integrated optics realized by surface-micromachining”,International Journal of High Speed Electronics and Systems 8, WorldScientific, 283-97 (1997); and M. F. Chang, M. C. Wu, J. J. Yao, M. E.Motamedi, “Surface micromachined devices for microwave and photonicapplications”, Proceedings of the SPIE—The International Society forOptical Engineering, (Optoelectronic Materials and Devices) 3419, M.Osinski, Y. Su, chairs/editors, 214-26 (1998).

[0016] Refractive microlenses have further been used inspectrophotometry. See, for example, S. Traut, H. P. Herzig,“Holographically recorded gratings on microlenses for a miniaturizedspectrometer array”, Optical Engineering 39, 290-8 (2000).

[0017] Refractive microlenses have still further been used in confocalmicroscopy. See, for example, M. Eisner, N. Lindlein, J. Schwider,“Confocal microscopy with a refractive microlens-pinhole array”, OpticsLetters 23, 748-9 (1998).

[0018] Refractive microlenses have yet still further been used insensors. See, for example, P. Nussbaum, R. Volkel, H. P. Herzig, M.Eisner, S. Haselbeck, “Design, fabrication and testing of microlensarrays for sensors and Microsystems”, Pure and Applied Optics 6, 617-36(1997).

[0019] Refractive microlenses have yet still further been used in focalplane arrays. See, for example, M. E. Motamedi, W. E. Tennant, H. O.Sankur, R. Melendes, N. S. Gluck, S. Park, J. M. Arias, J. Bajaj, J. G.Pasko, W. V. McLevige, M. Zandian, R. L. Hall, P. D. Richardson,“Micro-optic integration with focal plane arrays”, Optical Engineering36, 1374-81 (1997).

[0020] Finally, refractive microlenses have been used inphotolithography. See, for example, P. Nussbaum, R. Volkel, H. P.Herzig, M. Eisner, S. Haselbeck, “Design, fabrication and testing ofmicrolens arrays for sensors and Microsystems”, Pure and Applied Optics6, 617-36 (1997).

[0021] In general, increasing applications for micro-optical elementspresent increasing applications for microlenses, and microlens arrays.To address this expanding need for microlenses, fabrication technologieswould desirably be identified that will permit precision microlensarrays to be constructed at low cost. In addition, these microlensarrays must be reliably uniform and reproducible so that they can beincorporated seamlessly into existing optical architectures and systems.

[0022] 2.1.1 Fabrication of Arrays of Microlenses by Other ThanHydrophobic Processes

[0023] At present, there are several methods used to form arrays ofrefractive microlenses. The most viable of these techniques include: (1)dispensed droplets, (2) thermal reflow, and (3) photothermal expansion.A brief description of each of these techniques follows:

[0024] In the dispensed droplets technique a modified ink-jet printer,or other dispensing mechanism is used to dispense precise volumes of apolymer material into an array of droplets which can serve asmicrolenses.

[0025] The dispensed droplet technique for fabricating microlens arraysdoes not utilize a lithographic step, and hence suffers from drawbacksin accuracy. Because of limitations in fluid-handling control,microlenses fabricated with this technique have relatively large minimumdiameters (typical values today ˜70 um). The pitch of the lenses mustalso be relatively large, to avoid overlap. Also, the footprints of thelenses thus created are always circular, unless the substrate ispre-patterned, or a special curing process is employed. Another drawbackto the technique of dispensed droplets is that it typically requiresheating of the dispensed material, making it incompatible with someheat-sensitive materials. In it's defense, the technique requires verylittle characterization, and few processing steps, making it low-cost.See for example W. R. Cox, D. J. Hayes, T. Chen, and D. W. Ussery,“Fabrication of micro-optics by microjet printing”, SPIE Vol. 2383, pp.110-115.

[0026] In the thermal reflow technique a substrate is coated with alayer of photoresist. The resist is patterned to form an array of resist“islands”. The substrate is then heated until the resist melts andsurface tension draws the islands of resist into the shape of thelenses. If desired, this pattern can then be transferred to theunderlying substrate with a reactive ion etch (RIE). Gray scale maskscan be used to further extend the capabilities of the thermal reflowprocess. The use of gray level masks allows the fabrication of“photoresist sculptures”, which can, in principle, be used to fabricatealmost any desired lens shape with excellent precession.

[0027] Thermal reflow techniques have been used to generate extremelyuniform arrays of microlenses with arbitrary footprint shapes. Thelenses are lithographically defined, and hence the size, shape, andpitch of the lens arrays can be controlled to within 0.1 um. Howeverthere are several drawbacks to this technique. First, it requiresextensive characterization of the reflow process, including carefulcontrol of resist thickness, and exposure times, and the temperature,and heating times at which the reflow process is conducted. Second,since photoresist is opaque at many wavelengths of interest, it is oftennecessary to transfer the lens pattern to an underlying substrate, usingan RIE. This again requires careful characterization. Because of thecomplications involved in characterizing the reflow process and thesubsequent RIE, the technique is somewhat costly. See for example,Kufner, Maria and Stefan, Micro-optics and Lithography, VUBPRESSS,Brussels, 1997, pp 81-118, 183-184. See also Herzig, Hans Peter,Micro-Optics Elements, Systems and Applications, Taylor & Francis Ltd,Bristol, Pa., 1997, pp. 127-152. See also Sinzinger, Stefan, and Jahns,Jurgen, Microoptics, Weinheim, N.Y., 1999, pp. 85-123.

[0028] Finally, in the photothermal expansion technique certainmaterials (glasses, polymers), experience a local volume change whenexposed to certain kinds of high intensity radiation. UV x-ray,electron, and proton beams have all been used to induce local volumechanges in various materials, with the result that the exposed materialis “squeezed” into a quasi-spherical lens shape.

[0029] Photothermal expansion techniques require particularphotosensitive materials, and a high-energy radiation source, both ofwhich impose cost and materials constraints. There also are limitationson the shape that the lenses can assume, and a post-exposure polish isoften needed to ensure optical quality of the lenses. See for example,Kufner, Maria and Stefan, Micro-optics and Lithography, VUBPRESSS,Brussels, 1997., pp 81-118, 183-184. See also Herzig, Hans Peter,Micro-Optics Elements, Systems and Applications, Taylor & Francis Ltd,Bristol, Pa., 1997, pp127-152. See also Sinzinger, Stefan, and Jahns,Jurgen, Microoptics, Weinheim, New York, 1999, pp. 85-123.

[0030] 2.1.2 Fabrication of Arrays of Microlenses by HydrophobicProcesses

[0031] Several authors have proposed and demonstrated techniques whichenable the fabrication of microlens arrays by use of the hydrophobiceffect. See M. E. Motamedi, et al., supra; P. Nussbaum, et al., supra;and also E. Kim and G. M. Whitesides, “Use of Minimal Free Energy andSelf-Assembly To Form Shapes”, Chem. Mater. 7, 1257-1264 (1995).

[0032] The present invention will be seen to be a modification of theseprevious techniques in that, inter alia, microlenses will be assembledby use of hydrophilic domains patterned in an adhesive (rather than achemically-bonded) hydrophobic layer. Polymer microlenses in accordancewith the present invention will be seen to be readily fabricated on auseful variety of substrates, including glass (SiO₂), Si, SiN, GaAs,InGaAs, and InP. See D. M. Hartmann, O. Kibar, S. C. Esener,“Characterization of a Polymer Microlens Fabricated Using theHydrophobic Effect”, Optics Letters 25, 975-977 (2000).

[0033] The present invention will also be seen to be different from thesuggested processes of these papers because, inter alia, it has beenrecognized that the focal length of the microlenses can be controlled byadjusting any of a number of parameters during the fabrication process.These parameters include the substrate tilt angle and withdrawal speed(if the lenses are formed by a process of withdrawing the substrate froma liquid bath), the liquid viscosity, surface tension, density, andindex of refraction, the fill factor of lens arrays, and thesurface-free-energy of the hydrophilic and hydrophobic regions of thesubstrate.

[0034] The present invention will still further be seen to be differentfrom the suggested processes of these papers because it allows strong(low f-number) lenses to be fabricated via multiple dip-coats, ormultiple rounds of condensation.

[0035] The present invention will yet still further be seen to bedifferent from the suggested processes of these papers because, interalia, it may employ a unique self-alignment strategy, as immediatelynext discussed.

[0036] 2.2 Aligning Microlenses to Optical Components, and DirectFabrication of Microlenses on Optical Components

[0037] There is a further present requirement to position microlenses inalignment to optical components. In particular, as optical systems havebecome more widespread increasing interest has arisen in the placement,or fabrication, of microlenses on or in precise spatial relationship tooptically active devices such as vertical cavity surface emitting lasers(VCSELs), light emitting diodes (LEDs), and detectors, as well asdirectly upon passive components such as optical fibers. Suchmicrolenses are used in coupling or guiding light from one opticalcomponent to another within an optical system.

[0038] Techniques for fabricating microlenses on or in fixed spatialrelationship to other optical components naturally fall into twodifferent categories: those in which the microlens is fabricateddirectly on the optical component, and those in which the microlens isfabricated externally, and is then aligned to the component of interest.Direct fabrication of microlenses has the advantage that the opticalcomponents themselves often define the footprints of the fabricatedmicrolenses. For example, resist-reflow, ink-jet printing, anddeep-proton irradiation have all been used to fabricate microlensesdirectly over the apertures of LEDs, VCSELs, and optical fibers usingthe apertures to define the microlens diameters. See, for example, P.Heremans, J. Genoe, and M. Kuijk, IEEE Photonics Tech. Letters 9, 1367(1997); E. Park, et al., IEEE Photonics Technology Letters 11, 439(1999); and M. Kufner, Microsystem Technologies 2, 114 (1996).

[0039] Similarly, microlenses have been fabricated on the ends ofoptical fibers by wet etching, laser ablating, or melting the ends ofthe fibers to produce microlenses. See, for example, Johnson et al.,Proceedings of the SPIE 3740, 432 (1999); and Presby et al., AppliedOptics 29, 2692 (1990).

[0040] Such microlenses can greatly improve the coupling efficiency oftransmitters and detectors to optical fibers, and can even enhance thequantum efficiency of light-emitting devices. See, for example, P.Heremans, et al., supra; and also E. Park, et al., supra.

[0041] Direct fabrication of microlenses is useful when small opticalbeam diameters are acceptable. However free-space optical communicationsystems, optical switching systems, and many display and imagingapplications, require relatively large beam diameters so that the beamsdo not appreciably diffract as they propagate through the system. Insuch cases, microlenses must be fabricated externally, some distanceaway from the output apertures of the optical components. This in turnrequires careful alignment of the microlenses. Methods of performingsuch alignments include the use of precision grooves. See, for example,M. Rode and B. Hillerich, IEEE J. of Microelectromechanical Systems 8,58 (1999).

[0042] Methods of performing such alignments also include micro-opticalbenches. See, for example, Y. Aoki et al., Applied Optics 38, 963(1999); and also Y. Peter, Proc. of the SPIE 3513, 202 (1998).

[0043] Finally, methods of performing such alignments also includeactive-alignment using four-f imaging systems. The former schemes aresomewhat limited in that they require the optical components to beplaced into pre-fabricated structures, that have themselves beencarefully aligned. The later active scheme, while more versatile,requires expensive machinery and can be extremely time consuming. Whenlow f^(#) microlenses are desired, alignment tolerances become so tightthat the fabrication of microlenses aligned to optical components viaany of these techniques becomes economically impractical. This limitsthe f^(#) of microlenses that can be integrated and imposes minimum sizeconstraints on the optical systems in which the microlenses areincorporated.

[0044] The first part of the present invention will be seen to show anew method for the low cost precision fabrication of microlenses. Thesecond part of the present invention will show how, in an adaptation andextension of the base process, microlenses may be fabricated on, and inprecision spatial relationship to, optical components.

[0045] 2.3 Fabrication of Aligned Bump-bonds

[0046] Bump bonds, such as are commonly made with metal solders or withconductive polymer, must be aligned to the metal contact pads upon asubstrate that commonly also contains electrical circuitry. The presentinvention will be seen to show how bump bonds may be fabricated inself-alignment to metal contact pads.

[0047] Solder bump bonding is by far and away the most widely used meansof performing flip chip bonding. In the standard technique for placingsolder bumps, a layer of solder (10 um thick or more) is thermallyevaporated onto the chip, and lithographically patterned on top ofwettable “base-metal” bonding pads. These bonding pads are surrounded bya non-wettable dielectric passivation layer, known as a solder dam.After lithographically patterning the solder, the substrate is heated toreflow the solder so that it forms a spherical bump, whose footprint isdefined by the wettable base-metal pad area. A less-standard, but stillwidely used method of depositing the solder bumps is to electroplatethem onto the base-metal bonding pads. There has even been some workconducted in ink-jet printing solder bumps on a circuit.

[0048] Polymer bump-bonds have also been explored for use in circuits,and have several important advantages over more conventional solder-bumpbonds. These include a small size and weight, a reduction of processingcosts, low-temperature curing capabilities, and the ability to easilyrework flip-chip devices bumped with conductive adhesives.

[0049] Currently, there are several existing methods for fabricatingpolymer bump bonds. These include the use of stencils, screen-prints,and micromachining, to transfer a pattern of conductive polymer pasteonto a substrate. Stencils and screens require careful alignment withthe underlying bonding pads on the chip. The paste is then injectedthrough the screen onto the bonding pads. Micromachined polymer moldshave also been used to generate arrays of polymer bump bonds. Theresulting polymer bonds must then be aligned to their bonding pads.

[0050] Like solder bump bonding, the present invention utilizes awettable base-metal, surrounded by a non-wettable passivation layer todefine the footprint of the polymer bumps. Uniquely, however, the liquidis self-assembled on the wettable base-metal, and there is therefore noneed for any lithographic steps, reflow, or electroplating.

[0051] 2.4 Fabrication of Bonds Between Perpendicular Substrates, andOther Three-Dimensional Microstructures

[0052] It is difficult to fabricated electrical bonds between very smallfeatures at the edge regions of perpendicular substrates because it isdifficult to hold the substrates in precise alignment while the featuresare connected, such as by soldering of corresponding solder pads upontwo perpendicular substrates.

[0053] Still other three-dimensional microstructures, such as opticalfibers or light pipes, might usefully serve to connect correspondingregions upon different substrates that occupy different physical spaces,including perpendicularly proximate to one another.

[0054] The present invention will be seen to show the generation ofconnections and features, both electrical and optical, both (i) in situ,and (ii) self-aligned, between corresponding small, micro, domainslocated on different physical bodies, including substrates and boardsincluding as may be in a perpendicular relationship.

[0055] 2.5 Summary Attributes of the Prior Art

[0056] Accordingly, it is known to assemble, at least, microlenses byplacement of liquids onto hydrophilic domains within a hydrophobicbackground; no particular method of liquid transfer being, however,described. It is in particular known to deposit liquids on hydrophobicareas to form microlenses. See, for example, Use of Minimal Free Energyand Self-Assembly to Form Shapes, Enoch Kim and George M. Whitesides,Chem. Mater., 1995, 7, Pgs. 1257-1264. See also Microcontact Printing ofSelf-Assembled Monolayers: Applications in Microfabrication, James L.Wilbur, Amit Kumar, Hans A. Biebuyck, Enoch Kim, and George M.Whitesides, Nanotechnology 7m 1996, Pgs. 452-457.

[0057] It is also known to cure these liquids to form stable polymerstructures by ultraviolet (UV) light curing, by thermal curing, and byother means. See, for example, Kim and Whitesides, id.

[0058] The formation of microlenses by (i) pulling a substrate through apolymer/H₂O interface has in particular been described. See, forexample, Self-Organization of Organic Liquids on PatternedSelf-Assembled Monolayers of Alkanethiolates on Gold, Hans A. Biebuyckand George M. Whitesides, Langmuir 1994, 10, Pgs. 2790-2793. See alsoKim and Whitesides, id.

[0059] Microlenses have also been formed by (ii) putting a drop ofpolymer on the substrate and then tilting the substrate. See, forexample, Combining Patterned Self-Assembled Monolayers ofAlkanethiolates on Gold with Anisotropic Etching of Silicon to GenerateControlled Surface Morphologies, Enoch Kim, Amit Kumar, and George M.Whitesides, J. Electrochem. Soc., Vol. 142, No. 2, February, 1995 Pgs.629-633

[0060] Microlenses have still further been formed by (iii) firstcondensing water on the substrate and then depositing the polymersubsequently, so that the polymer goes only to the non-hydrophilic areasof the substrate. See, for example, Thin Microstructured Polymer Filmsby Surface-Directed film formation, H.-G. Braun, E. Meyer, appearing inThin Solid Films 345 (1999) Pgs. 222-228.

[0061] The present invention will be seen to use a process step otherthan (i) passing through a polymer/H₂O interface; or (ii) tilting; or(iii) condensing water/depositing polymer.

[0062] Quite logically, the prior art recognizes the use of microlensarrays to focus and correct aberrations in the intensity of light fromlasers or optical fibers. See, for example, Biebuyck and Whitesides, id.However, the location and alignment of the arrayed microlenses relativeto the light sources—as will be taught by the present invention—isproblematic.

[0063] Finally, it is also known in the prior art to use conductivepolymers for electrical connection, and to assemble the conductivematerials (the conductive polymers) by dip-coating on hydrophilicdomains. See, for example, Selective Deposition of Films of Polypyrrole,Polyaniline and Nickel on Hydrophobic/Hydrophilic Patterned Surfaces andApplications, Z. Huang, P. C. Wang, J. Feng, and A. G. MadDiarmid,Synthetic Metals 85 (1997) Pgs. 1375-1376.

[0064] However, to the best knowledge of the inventors, the prior artdeals exclusively with the use of conductive polymer to make electricalcontacts (that is, pads to which bump bonds may be attached). Thepresent invention will shortly be seen to contemplate another use: themaking of the bump bonds themselves.

SUMMARY OF THE INVENTION

[0065] The present invention contemplates the fabrication of precisionmicrostructures on a base—such as a planar substrate or the butt end ofan optical fiber—by (i) depositing a liquid material on hydrophilicdomains of a base of patterned wettability, followed by (ii) using thematerial left upon the hydrophilic domains, including as is most oftensolidified, as a microstructure.

[0066] The liquid is strongly preferably a liquid polymer precursor, ormonomer. In this case the liquid is solidified, or cured, afterdeposition to form a solid microstructure. However, the liquid—such asGlycerol—may remain a liquid, in which case the fabricatedmicrostructure—normally a microlens or bump bond or bond as hereinafterdiscussed,—remains liquid, ergo a liquid microlens or liquid “bump” bondor liquid bond.

[0067] The depositing strongly preferably occurs by action ofwithdrawing the base from a bath of the liquid but may, equivalently,arise by condensing the liquid on the patterned hydrophilic domains.

[0068] The microstructures so fabricated preferably include (i)transparent solid polymer microlenses including as may be either arrayedor (in another aspect of the invention) self-aligned to optical fibers,(ii) conductive bump bonds self-aligned (in another aspect of theinvention) to bump pads, and (iii) bonds between corresponding smalldomains on separate substrates, including as are most commonly mutuallyperpendicular.

[0069] The present invention further contemplates self-alignment: anadaptation of the fabrication process to produce microstructures thatare self-aligned to other micro-sized features, most commonly patterneddomains on a substrate, fiber or other physical body. For example,microlenses may be self-aligned at time of their fabrication to opticalfibers and low-wavelength broad-band and/or single-mode light sources.For example, bump bonds may be self-aligned at time of their fabricationto bump pads present upon a substrate.

[0070] This self-alignment is very useful: optically connective (e.g.microlenses) or electrically connective (e.g., bump bonds)microstructures end up on substrates, optical fiber ends, or wherever inexactly the desired locations. Consider, for example, the self-alignmentof bump bonds. The deposition of conductive polymers on metal contactpads contemplated by the present invention permits, by virtue of thefact that these metal contact pads are hydrophilic, the in-situfabrication of conductive bump bonds that are precisely and perfectlyaligned to metal contact pads—a non-trivial accomplishment when the padsand bonds are small.

[0071] The present invention still further contemplates the fabricationof bonds between metal contact pads on perpendicular substrates. Suchbonds are achieved through (i) the deposition of conductive polymers onthe contact pads of both substrates and (ii) the subsequent alignment ofthe substrates perpendicular to one another—in amotherboard/daughterboard fashion—such that the conductive polymers onthe two substrates contact one another in precise spatial locations,thereby establishing electrical connections between the two substratesat those locations. Heretofore this and other three-dimensional opticaland electrical interconnections contemplated by the present inventionwere difficult or impossible of practical realization.

[0072] 1. Fabrication of Polymer Microstructures by Hydrophobic Effect

[0073] The microstructures fabricated by the method of the presentinvention may be, for example, microlenses. In that case (i) a liquidpolymer precursor is deposited on the hydrophilic domains of a substrateof patterned wettability by action of, preferably, withdrawing thesubstrate from a bath of the liquid polymer precursor, followed by (ii)curing the liquid polymer precursor left upon hydrophilic domains intotransparent solid polymer microlenses by heat, ultraviolet light,chemicals or other conventional means.

[0074] Significantly, the most preferred fabrication method realizes the(i) depositing by dip coating. Moreover, the most preferred hydrophobiclayer is adhesive, rather than chemical.

[0075] Next, the present invention further contemplates that when and ifthe substrate is withdrawn from a liquid bath of polymer precursor—as ispreferred—to produce microlenses then the f-number (f^(#)) of themicrolenses so fabricated is precisely controllable by adjusting any of(i) liquid viscosity, surface tension, density, index of refraction andlike physiochemical properties; (ii) surface-free-energies of thehydrophilic and hydrophobic regions of the substrate; (iii) substratedipping angle; (iv) substrate withdrawal speed; (v) array fill factor;and/or (vi) number of dip coats used.

[0076] Being that, to the best knowledge of the inventors, they are thefirst to employ dip-coating in a hydrophobic process for the productionof microstructures including microlenses, they are the first torecognize that control of the substrate withdrawal speed, and dippingangle, monomer viscosity, surface tension, density, and index ofrefraction, and the array fill-factor, and the surface-free-energies ofthe hydrophilic and hydrophobic areas will permit control of the f^(#)of microlenses. Indeed, the same substrate can be withdrawn slowly atone time and quickly at another so as to create microlenses ofdramatically different f^(#) immediately adjacent to each other.

[0077] Moreover, the invention still further contemplates that multipledip-coats can be used to improve lens performance; a “faster” lens witha lower f^(#) resulting from multiple dipping/curing cycles. Clearly ifonly a portion of a substrate is re-dipped than only the microlenses ofthat portion will augmented.

[0078] The microlenses so precision fabricated are useful. They can befabricated with a range of f^(#)s (with a plano-convex minimum off/1.38), excellent surface profiles (maximum deviation from a sphere was<±5 nm over the center 130 μm of 500 μm diameter f/3.2 microlenses), andare stable at room temperature.

[0079] Fabrication of the microlenses is well controlled, and themicrolenses so fabricated are of uniform high quality. An optimumwithdrawal speed was identified at which (i) the f^(#) of each microlenswas minimized while (ii) uniformity of all microlens in the array wasmaximized. At this optimum speed arrays of f/3.48 microlenses werefabricated using one dip-coat with uniformity better than Δf/f˜±3.8%.Multiple dip-coats allowed production of f/1.38 microlens arrays anduniformity better than Δf/f˜±5.9%. Average f^(#)s were reproducible towithin 3.5%.

[0080] Although inventors are not charged to know the theory of theirinvention, a model of the process of the present invention has beendeveloped. This model, describing the fluid transfer process by whichliquid solution assembles on the hydrophilic domains, accuratelydescribes real-world results. By use of the model microlenses of anyreasonably desired properties may be fabricated, including with massiveparallelism.

[0081] 2. A Method of Fabricating Polymer Microlenses

[0082] Accordingly, in one of its aspects the present invention isembodied in a method of fabricating polymer microlenses.

[0083] The method consists of depositing liquid on the hydrophilicdomains of a substrate of patterned wettability. Liquid transfer may beachieved by withdrawing the substrate from a liquid bath (dip-coatingthe substrate), or by condensing the liquid. In either case, the liquidcollects in hydrophilic areas of the substrate and forms caps of theliquid which may then be (optionally) cured so as to form solidmicrolenses.

[0084] By adjusting at least one of (i) liquid viscosity, surfacetension, density, and index of refraction (ii) the surface-free-energiesof the hydrophobic and hydrophilic areas of the substrate, (iii) theangle of the substrate withdrawal, (iv) the speed of the withdrawing ofthe substrate, (v) the proximity of hydrophilic areas one to the next,and/or (vi) the number of times the dip-coating or condensation isperformed, the process may be controlled to allow the f-number (f^(#))of the resulting microlenses to be predictably and repeatablycontrolled. The process is preferably controlled in all theseparameters, which may be varied during the fabrication of multiplemicrolenses upon a single substrate so as to vary the properties, mostnotably the f^(#), of the microlenses.

[0085] 3. A Detailed Method of Fabricating Polymer Microlenses

[0086] In greater detail, in the method of the present invention forfabricating polymer microlenses a hydrophobic layer is first applied toa substrate. This hydrophobic layer can be, and preferably is, adhesivein nature, in which case it can be applied by mechanically polishing thesubstrate with the hydrophobic material or by spinning the hydrophobiclayer onto the substrate. More conventionally, this hydrophobic layercan also be chemical in nature, in which case it can be applied bymicro-contact printing (as taught by Whitesides, et al., id.), or bysurface modification in a chemical bath. The substrate may be anymaterial that can be appropriately chemically modified, or to which thehydrophobic layer will adhere. Substrates on which deposition of ahydrophobic layer, and subsequent fabrication of microlenses (by methodof the present invention), have been demonstrated include glass, Si,SiO2, SiN, GaAs, InGaAs, or InP. Other substrates may also be suitable.

[0087] The hydrophobic layer is patterned, so as to produce a pluralityof hydrophobic, and hydrophilic, areas. The layer is patterned with adesired level of accuracy (typically lithographic accuracy). If thehydrophobic layer is applied to the full substrate, it can be patternedby standard lithography. Alternatively, micro-contact printing (seeWhitesides, et al., id.) or similar techniques can be used to depositpre-formed patterns of hydrophobic material with lithographic accuracy.Finally, if the hydrophobic layer is applied to a substrate consistingof two or more materials, and the hydrophobic layer is properly chosenso that it adheres or bonds to all but one of the materials, then thehydrophobic layer is patterned by virtue of the underlying materialheterogeneity. The accuracy of the hydrophobic patterning then dependson the accuracy with which the heterogeneous substrate was originallyfabricated.

[0088] Liquid is next allowed to assemble on the substrate with itsselectively patterned hydrophobic layer. Liquid may be transferred tothe substrate by one of two means. First, liquid may be condensed ontothe hydrophilic areas of the substrate. Second, and preferably, thesubstrate may be dipped into a liquid bath and then controllablywithdrawn from the solution so that, as the substrate is withdrawn, theliquid drains from the hydrophobic areas of the substrate but remains onthe hydrophilic areas. For the fabrication of homogeneous structures theparameters, including the speed, of the withdrawal remain constant.However, if different properties are desired in the polymer structuresthat will be created in different regions of the substrate then theparameters of the withdrawal, most notably including the speed ofwithdrawal, can be varied. The dip-coating method is preferred becauseof the excellent, and wide-ranging, control over the liquid-depositionprocess that it affords.

[0089] Regardless of which method is used to transfer liquid to thesubstrate, the liquid clings to the hydrophilic areas, and forms caps ofliquid under the influence of surface tension. These caps will adopt ashape that minimizes their free energy.

[0090] The caps may be used as lenses in their liquid form. Such liquidlenses have potential for use as variable focusing lenses. Alternativelyif the liquid that comprises the lenses is a curable-solution, (e.g. amonomer solution), then the caps of curable monomer present upon thesubstrate may be cured so as to make one or a plurality of solid polymermicrolenses. The liquid monomer may be cured by ultraviolet (UV) lightor other optical curing methods. The liquid monomer may alternatively becurable by evaporation of a solvent, or by heat or time-induced changesin chemical structure of the monomer.

[0091] The lithographic patterning of the hydrophobic layer into aplurality of regularly geometrically sized and related areas can beconducted so that the plurality of microlenses ultimately formed by thecuring are in a regular array. A great number of microlenses may befabricated with massive parallelism.

[0092] Importantly, this base method may be extended to (i) re-dippingthe substrate with its plurality of polymer microlenses into the liquidmonomer solution so that additional monomer solution accrues on top ofthe existing cured microlenses (ii) re-withdrawing the substrate fromthe solution, and, (iii) re-curing the newly-added curable monomerpresent upon the plurality of microlenses (which are upon the substrate)so as to make an augmented microlenses having a decrease in the radii ofcurvature, and a corresponding reduction in f^(#). By repetitivelyre-dipping, re-withdrawing and re-curing, microlenses of any(reasonably) desired low f^(#) may be produced. Similarly, instead ofre-dip-coating the substrate, additional rounds of liquid condensationand curing may be performed. However, dipping is particularly easilymanipulated to produce different microlenses—particularly as comprisedifferent materials, or as have different f^(#)'s—in different regionsof the same substrate. This is realized simply by selectively dippingand re-dipping certain regions, optionally into selective solutions. Forexample, microlenses of different colors can be created on the samesubstrate.

[0093] 4. Fabrication of Self-aligned Microlenses

[0094] An important adaptation and extension of the base method of thepresent invention for fabricating microlenses permits the production ofmicrolenses that are self-aligned to optical fibers and/orlow-wavelength single-mode optical transmitters. The adapted andextended method can be used to self-align microlenses directly on theoptical components or, further uniquely, on transparent spacers thatserve to separate the microlenses from the components.

[0095] Because the microlenses are self-aligned, low f^(#) microlensesthat would otherwise require tight alignment tolerances can beintegrated with ease. As an example, f/1.55 microlenses with smoothsurface profiles, deviating from spherical by just ±15 nm, have beenintegrated on SMF optical fiber. Arrays of such microlenses havingexcellent uniformity (Δf/f˜5.9% for a 15×15 array of 500 μm f/1.4microlenses), stability, and reproducibility (average f^(#)s arereproducible to within 3.5%) can be fabricated with massive parallelism.

[0096] 4.1 Detail Method of Fabricating a Microlens Precision Sized,Aligned and Spatially Positioned to a Small Light Source

[0097] In detail, the method of the present invention for fabricating amicrolens that is precisely (i) sized, (ii) aligned and (iii) spatiallypositioned to a small light source proceeds as follows:

[0098] A small light source—such as a vertical cavity surface emittinglaser (VCSEL), light emitting diode (LED), or a passive component suchas an optical fiber that is coupled to some light source so as to emitlight at one end—is affixed—by transparent adhesive or other means—to atransparent “spacer element” having a surface on which is present ahydrophobic layer and a photoresist layer. The light output of the smalllight source is directed onto this surface of the transparent “spacerelement”. (The “spacer element” is so called because, ultimately, itwill serve to space the small light source from a microlens that is yetto be created.)

[0099] Next, the surface of the spacer element is patterned. This occursby (i) exposing the photoresist with, only at the light output of, thesmall light source, then (ii) etching away the hydrophobic layer at andfrom the exposed region (such as with O₂ plasma), and then (iii)stripping remaining photoresist so as to leave a hydrophilic domain in ahydrophobic background sized, shaped and juxtaposed relative to thelight output of the light source.

[0100] Next, a microlens is formed upon the patterned surface of thespacer element. This occurs by transferring liquid to the hydrophilicdomain by condensing liquid on the domain, or by (i) immersing thesurface-patterned spacer element in an (optionally curable) liquidsolution, then (ii) withdrawing the spacer element from solution so asto leave in the hydrophilic area of its patterned surface a liquid cap,followed by (iii) optionally curing the liquid cap to form a solidmicrolens. As with the base method of the present invention, the (i)immersing and the (ii) withdrawing and the (iii) curing may be repeatedso as to form a microlens of any (reasonably) desired low f^(#).Similarly, successive rounds of condensation and curing may be usedrepeatedly so as to form a microlens of any (reasonably) desired lowf^(#).

[0101] By these steps, a microlens is created upon the surface of thespacer element in a position juxtaposed to the light source, and in ashape and a size of the light output from the light source. Theprecision microlens so created is useful to guide light emitted from thelight source (which light is first received into the affixed transparentspacer element).

[0102] The transparent spacer element is most commonly a rectilinearsubstrate (such as a glass slide), and a great number of microlenses asserve to couple the light outputs of a corresponding great number oflight sources (such as VCSELs upon the substrate of a hybridoptoelectronic circuit) can be fabricated all at the same time, and inparallel.

[0103] The intensity and/or the duration, and preferably both theintensity and the duration, of the light output of each small lightsource is controlled so as to control the size of an area of thephotoresist that is exposed, and subsequently etched. Note that not alllight sources, even if of the same type, have to be equally illuminated(so as to cause equal-size areas of exposed photoresist and, ultimatelyand other parameters remaining constant, equally-sized microlenses).Note that an area may be illuminated where a microlens will never bemade, and where no optical coupling will ever ensue; the area beinginstead used for a conductive polymer electrical connection bump pad. Itis clear the present invention accords flexibility in fabrication ofpolymer microstructures—even as transpires upon the same substrate atthe same time, or during related steps at sequential times.

[0104] The area of the microlens ultimately formed on the surface of thespacer element is thus controllable. Note also that the light outputfrom the light source, especially as appears at the end of an opticalfiber may be, and commonly is, controlled to be more intense and/or morepersisting than will be another beam, normally for communicationspurposes, employed during a future usage of the fiber in an opticalsystem; the more intense and/or more persistent photoresist exposurebeam making the ultimately resulting lens to be desirably “oversize” forand in its actual system usage (i.e., so that the actual system's lightbeam under-fills the lens).

[0105] 4.2 Detail Method of Fabricating a Microlens Directly Upon theEnd of an Optical Fiber

[0106] In detail, the method of the present invention for fabricating amicrolens upon the butt end of an optical fiber proceeds as follows:

[0107] The butt end of an optical fiber is coated first with ahydrophobic material and then with a photoresist.

[0108] Hydrophobic material is then patterned upon the coated opticalfiber end by (i) exposing the photoresist with light output from theoptical fiber source, then (ii) etching away the hydrophobic material atand from the exposed region, and then (iii) stripping remainingphotoresist so as to leave a hydrophilic domain sized and shapedrelative to the light output of the optical fiber.

[0109] Finally, a microlens is formed upon the patterned optical fiberend. This transpires by either condensing liquid on the hydrophilicdomain or by (i) immersing the patterned optical fiber end in an(optionally curable) liquid, then (ii) withdrawing the optical fiber endfrom the liquid so as to leave in the hydrophilic area of the opticalfiber end a liquid cap, and then (iii) optionally curing the liquid capto form a solid microlens.

[0110] As with the base method of the present invention, the (i)immersing and the (ii) withdrawing and the (iii) curing may be repeatedso as to form a microlens of any (reasonably) desired low f^(#).Similarly, successive rounds of condensation and curing may be usedrepeatedly so as to form a microlens of any (reasonably) desired lowf^(#).

[0111] By these steps a microlens is located upon the optical fiber endin a shape, and in a size of, light that is output from the opticalfiber. This precision microlens is useful to guide this light outputfrom the optical fiber. The method may be performed in parallel on agreat number of optical fibers.

[0112] 5. A Method of Fabricating Conductive Polymer Bump Bonds

[0113] The present invention further contemplates utilizing the samefundamental technology to produce conductive polymer bump bonds that areself-aligned to underlying metal contact pads.

[0114] 5.1 Detail Method of Fabricating Conductive Bump BondsSelf-aligned to Contact Pads

[0115] In yet another of its aspects the present invention is embodiedin a method of fabricating conductive bump bonds self-aligned to contactpads.

[0116] The fabrication of bump bonds occurs by applying a hydrophobiclayer to a heterogeneous substrate (consisting of two or more materials)such that at least one material on the substrate remains hydrophilic,followed by the transfer of liquid to the hydrophilic areas of thesubstrate through condensation of the liquid on the hydrophilic domainsor by immersing the substrate in an (optionally) curable liquidsolution, and then withdrawing the substrate from the liquid so as toleave in the hydrophilic areas of the substrate caps of the liquid, thatmay be (optionally) cured to form a solid conductive bump bond,self-aligned to the hydrophilic domains on the heterogeneous substrate.

[0117] The present invention will be seen to facilitate the fabricationof bump bonds by a method similar to the method of microlensfabrication. Specifically, a heterogeneous substrate, consisting ofcontact pads of one material patterned within a background of a secondmaterial is used. A hydrophobic layer that preferentially adheres orchemically bonds to all parts of the substrate except the contact padsis then applied. Thus, the contact pads are left hydrophilic, while theremainder of the substrate is made hydrophobic. Liquid is thentransferred onto the hydrophilic contact pads. The transfer of liquidmay be achieved (1) by condensing the liquid onto these hydrophilicdomains, or (2) by withdrawing the heterogeneous substrates of patternedwettability from the liquid solution, whereby liquid drains from thehydrophobic areas of the substrate and remains on the hydrophiliccontact pads. Following liquid transfer, the liquids may be solidifiedby a process of curing or solvent-evaporation to produce bump bonds.These bump bonds may be conductive immediately upon curing, or mayrequire post-curing treatment (such as with acid-treatment) to cause thebonds to become conductive. Because the hydrophilic areas of thesubstrate are the contact pads where the bump bonds are desired, thebump bonds are fully self-aligned to these contact pads.

[0118] 6. A Method of Fabricating Conductive Polymer Bonds BetweenMutually Perpendicular Substrates

[0119] The present invention still further contemplates utilizing thesame fundamental process of the invention to produce conductive polymerbonds that are self-aligned to underlying metal contact pads and whichcan be used to electrically connect mutually perpendicular substrates.It is normally sufficient to pattern a substrate, or board, which willbe mounted edge-on only on its major surface (or surfaces). However,like as the patterning of the butt end of an optical fiber, the edgeside of a board or substrate can be patterned, or additionallypatterned, if desired or required (to make particularly exactingelectrical and/or mechanical connections).

[0120] The fabrication of electrical contacts between substratespreferably occurs by (i) patterning a hydrophobic layer on each of twoheterogeneous substrates such that at least one corresponding domain oneach substrate remains hydrophilic. Then transpires, in either order,(iii) transferring a liquid conductive-polymer-precursor to thehydrophilic areas of both substrates, and (ii) bringing the substratestogether so that one or more corresponding domains on each substrate areproximate. In other words, the liquid may be first applied to eachsubstrate, and the substrates then brought together—as is preferred—orelse the substrates may be brought proximate to each other and theliquid then applied to both in common.

[0121] Finally, transpires (iv) curing of the liquidconductive-polymer-precursor so as to bond the two substrates togetherwith electrical connection between corresponding domains on eachsubstrate. The actual physical attachment of the substrates is normallymade by a frame, or by epoxy adhesive, but, depending upon numbers andsize, the polymer bonds may provide physical, as well as electrical,attachment.

[0122] These and other aspects and attributes of the present inventionwill become increasingly clear upon reference to the following drawingsand accompanying specification.

BRIEF DESCRIPTION OF THE DRAWINGS

[0123] Referring particularly to the drawings for the purpose ofillustration only and not to limit the scope of the invention in anyway, these illustrations follow:

[0124]FIG. 1, consisting of FIGS. 1a through 1 f, is a diagrammaticrepresentation of the flow of the method of the present invention forthe hydrophobic patterning of microlenses.

[0125]FIG. 2 is a graph of f^(#) vs. substrate withdrawal speed for 500μm-diameter microlenses (fill factor˜0.24 ), for Sartomer CD541 andSartomer SR238 monomer solutions, and a glycerol solution.

[0126]FIG. 3 is a Table 1 listing the minimum f^(#) and the speed atwhich the minimum f^(#) is formed for several monomer solutions and aglycerol solution, particularly for 500 μm diameter microlenses with anarray fill factor ˜0.25.

[0127]FIG. 4 is a graph of f^(#) of 100 μm diameter microlenses madewith Sartomer CD541 (μ˜440 cP) monomer solution, vs. area ratio(hydrophilic area:hydrophobic area) for various withdrawal speeds.

[0128]FIG. 5 is a graph of f^(#) of 100 and 250 μm diameter microlensesmade with Sartomer CD541 (μ˜440 cP) monomer solution, vs. area ratio(hydrophilic area:hydrophobic area) for various withdrawal speeds.

[0129]FIG. 6 is a graph of f^(#) for 50 μm-diameter microlenses versusthe position of the microlens in a row of 188 microlenses, as measuredfrom one of the edges of the row.

[0130]FIG. 7 is a graph of Δf/f vs. substrate withdrawal speed for 500μm diameter microlenses (fill factor˜0.25), made with Ciba 5180 (μ˜200cP), and Sartomer CD541 (μ˜440 cP) monomer solutions.

[0131]FIGS. 8a and FIG. 8b are optical microscope pictures of thesurface of a 50 μm diameter microlens of, respectively, ˜f/3.5 made withone dip coat, and ˜f/1.6 made with two dip coats.

[0132]FIGS. 8c and FIG. 8d are Atomic Force Microscope (AFM) picturesof, respectively, the microlenses of FIGS. 8a and 8b.

[0133]FIG. 9 is a diagrammatic representation of a three-phase contactline as it rolls-off the substrate; the contact line is symmetrical inthe middle and asymmetrical at the edges.

[0134]FIG. 10, consisting of FIGS. 10a through 10 f, is a diagrammaticrepresentation of the flow of the adapted, and extended, method of thepresent invention for producing microlenses self-aligned to opticalfibers through a transparent spacer.

[0135]FIG. 11a is a microphotograph of a resist hole on 1.0 mm spacerglued to fiber made with white light exposure; a V-groove that the fiberrests in being visible.

[0136]FIG. 11b is a microphotograph of a 175 μm microlens on 1.0 mmglass spacer self-aligned to optical fiber; a V-groove that the fiberrests in again being visible.

[0137]FIG. 11c is a microphotograph close up of a microlens made inaccordance with either the base, or extended, methods of the presentinvention.

[0138]FIG. 12 is an error map of the profile of an exemplary microlensmade in accordance with the extended method of the present invention,the error map showing deviation from spherical of the middle 50 μm of a175 μm-diameter f/1.5 microlens that has been self-aligned to an opticalfiber.

DESCRIPTION OF THE PREFERRED EMBODIMENT

[0139] The following description is of the best mode presentlycontemplated for the carrying out of the invention. This description ismade for the purpose of illustrating the general principles of theinvention, and is not to be taken in a limiting sense. The scope of theinvention is best determined by reference to the appended claims.

[0140] Although specific embodiments of the invention will now bedescribed with reference to the drawings, it should be understood thatsuch embodiments are by way of example only and are merely illustrativeof but a small number of the many possible specific embodiments to whichthe principles of the invention may be applied. Various changes andmodifications obvious to one skilled in the art to which the inventionpertains are deemed to be within the spirit, scope and contemplation ofthe invention as further defined in the appended claims.

[0141] 1. Fabrication of Microlens Arrays

[0142] In accordance with the present invention, large and uniformarrays of microlens of controlled optical properties may be reliablyreproducibly fabricated.

[0143] Following section 1.1 describes the characterization andoptimization of microlenses, and microlens arrays, fabricated by themethod of the present invention. Arrays of microlenses with footprints2-500 μm in diameter were fabricated by withdrawing substrates ofpatterned wettability from a monomer bath at a controlled speed. Thefabricated arrays had lithographically-defined pitches, allowingfill-factors up to 90%. At low withdrawal speeds the average f^(#) offormed microlenses could be reduced by increasing substrate withdrawalspeed or monomer viscosity, or by decreasing monomer surface tension. Atlarger withdrawal speeds, the average f^(#) was minimized and becameconstant, independent of withdrawal speed. This minimum achievable f^(#)could be reduced by using a monomer with a large viscosity and largesurface tension. At all withdrawal speeds, the f^(#)s of formedmicrolenses could be reduced by decreasing the array fill factor or bytilting the substrate so that its patterned side was tilted up duringthe withdrawal process. Control of the withdrawal speed duringfabrication permitted integration of microlenses having different f^(#)swithin the same array. The uniformity of microlens arrays was analyzedin terms of defect density and microlens-to-microlens variability. Thenumber of conjoined microlenses could be minimized by reducing the arrayfill factor, monomer viscosity, and substrate withdrawal speed. Inarrays with no defects, an optimum withdrawal speed was shown to existat which array uniformity was maximized (i.e. the % change in the focallength across an array was minimized). At this optimum, arrays of f/3.48microlenses were fabricated using one dip-coat with a uniformity betterthan Δf/f˜±3.8%. Multiple dip-coats allowed production of arrays off/1.38 microlenses with uniformity better than Δf/f˜5.9%. Average f^(#)swere reproducible to within 3.5%. These values are competitive withthose of leading microlens fabrication technologies. Finally, othermicrolens characteristics, such as the diameter, shape, and surfaceroughness of the microlenses were shown to be excellent, and independentof the fluid transfer process.

[0144] Next following section 1.2 describes a model of the process ofthe method of the present invention. The model in particular describesthe fluid transfer process by which monomer solution assembles on thehydrophilic domains, forming microlenses under the influence of surfacetension. Specifically, equations which describe the fluid transferprocess on homogeneous hydrophilic and hydrophobic substrates are given,and these equations are merged to give an approximate solution for fluidtransfer onto a heterogeneously wettable substrate. Although theresulting equations are derived from the analysis of homogeneoussubstrates, and are therefore inexact for the heterogeneous case, theynonetheless provide insight into the forces governing themicrolens-forming process.

[0145] Next following section 1.3 sets forth theoretical predictions ofmicrolens characteristics which have been compared with actual results,with good agreement being found. The conditions that can be used tofabricate optimal microlens arrays are stated.

[0146] Finally, in the last following section 1.4 the results of thebase method of the invention are summarized.

[0147] 1.1 Fabrication and Characterization of Microlens Arrays

[0148] The preferred method of the present invention for the fabricationof microlens arrays is diagrammatically illustrated in FIG. 1,consisting of FIG. 1a through FIG. 1f.

[0149] An adhesive hydrophobic layer is mechanically applied to thesubstrate with a polishing cloth. The substrate is then lithographicallypatterned and the hydrophobic layer selectively etched away from theexposed regions. The substrate is then dipped into and withdrawn from aUV-curable-monomer solution at a controlled speed. As the substrate iswithdrawn, the monomer solution drains from the hydrophobic areas of thesubstrate but remains on the hydrophilic domains. The remaining solutionforms spherical caps under the influence of surface tension and can beUV-cured to form environmentally stable microlenses.

[0150] After curing, if stronger (lower f^(#)) microlenses are desired,the substrate may be re-dipped into the monomer solution. Additionalmonomer solution assembles on top of the existing cured microlenses,causing an increase in the radii of curvature, and a correspondingreduction in f^(#). This process of curing and re-dipping the substratemay be used repeatedly to reduce the f^(#) of the fabricatedmicrolenses.

[0151] For consistency, glass microscope slides were used as substratesfor all results reported in this specification. All monomer solutionsused had a density of ˜1.08 g/cm³. Once UV-cured, all polymers had anindex of refraction of approximately ˜1.5.

[0152] After fabrication, the microlenses were characterized.Fifteen—twenty microlenses were selected across a row of the microlensarray under test, and their focal lengths were measured. From thesemeasurements, the average f^(#) and the standard deviation of the focallength for the array were determined. The average f^(#) was plotted as afunction of the variable to be studied, and error bars were includedrepresenting one standard deviation from the average value. Aftercompleting one set of measurements, the substrate could be re-dippedinto monomer solution, withdrawn at a new speed, and the samemicrolenses could then be measured.

[0153] For a given monomer solution, at low withdrawal speeds,increasing substrate withdrawal speed results in a decrease in the f^(#)of formed microlenses. At these speeds, increasing monomer viscosity ordecreasing monomer surface tension also results in lower f^(#)s at anygiven withdrawal speed. These trends can be seen in FIG. 2, which showsaverage f^(#) vs. withdrawal speed for an array of 500 μm-diametermicrolenses for two monomer solutions and a glycerol solution. ASartomer CD541 monomer solution has a high viscosity, μ, of ˜440centipoise (cP) and a low surface tension, σ, of ˜35.3 dynes/cm, andgives rise to the smallest f^(#)s at all withdrawal speeds shown in FIG.2. A glycerol/H₂O solution, with a large viscosity (μ˜450 cP) and alarge surface tension (σ ˜64 dynes/cm) gives rise to slightly largerf^(#)s. Finally, a Sartomer SR238 monomer solution has a low viscosity(μ˜9 cP) and a low surface tension (σ˜35.7 dynes/cm) and gives rise tovery large f^(#)s.

[0154] For a given monomer solution, as withdrawal speed is furtherincreased, the f^(#) reaches a minimum value after which it increasesslightly and thereafter remains constant, independent of furtherincreases in withdrawal speed. FIG. 2 shows this minimum (f/˜2.5) forthe Sartomer CD541 monomer solution occurring at a withdrawal speed of˜800 μm/s. Both the minimum value of the f^(#) that can be achieved andthe withdrawal speed at which it occurs are functions of the surfacetension and viscosity. FIG. 3 is a Table 1 showing the minimumachievable f^(#) and the speed at which it occurs for several monomersolutions and a glycerol/H₂O solution. It can be seen from the Table 1that the smallest minimum f^(#)s can be achieved for solutions withlarge viscosities and large surface tensions.

[0155] For a given monomer solution, the average f^(#) of the formedmicrolenses decreases as the fill-factor of the array decreases (i.e. asthe ratio of hydrophilic:hydrophobic area decreases) Shown in FIG. 4 isa graph illustrating this trend for an array of 100 μm-diameter circularmicrolenses, fabricated from the Sartomer CD541 monomer solution atseveral different substrate withdrawal speeds.

[0156] The average f^(#) of the formed microlenses also depends greatlyon the shape of the domains. Because of the large number of possiblegeometric domain shapes, we have not attempted to quantify thedifferences between various microlens shapes (circular, square,elliptical, etc.). Rather, for consistency, we have used circulardomains in characterizing the parameters that affect microlensformation. For circular domains, the domain diameter does notsignificantly influence the achievable microlens f^(#) provided that thearray fill factor is maintained constant (although there are minordifferences at low withdrawal speeds). FIG. 5 illustrates this fact for100 and 250 μm diameter microlenses, where the average f^(#) at variouswithdrawal speeds is plotted as a function of the array fill factor.

[0157] The average f^(#) of the formed microlenses is also dependentupon the angle with which the substrate is withdrawn from the monomerbath. If the substrate is withdrawn such that its patterned face istilted up, the f^(#) of formed microlenses is reduced. Conversely, ifthe patterned face is tilted down, the f^(#) of formed microlenses isincreased. For consistency, all substrates in the experiments weconducted were withdrawn from the monomer solution vertically (with 0degrees tilt).

[0158] When all other conditions (i.e. substrate material, withdrawalangle, monomer solution, microlens shape and diameter, and arrayfill-factor) are held fixed, the f^(#) of a fabricated microlens dependsonly upon the speed with which the substrate is withdrawn from themonomer solution. By varying the substrate withdrawal speed during thewithdrawal process, different f^(#)s can therefore by integrated in thesame array in close proximity. This allows the implementation of avariety of optical architectures in which it is desired that differentrows in an array of microlenses have the same diameters but differentf^(#)s.

[0159] In addition to the f^(#) of the microlenses, the uniformity ofmicrolenses within an array is a parameter of interest. Analysis of theuniformity of a microlens array requires consideration of both thenumber of defects (lenses which are joined together, missing, ormisshapen) within the array, and an analysis of the uniformity of thosemicrolenses that are not defective.

[0160] The number of conjoined microlenses within an array is a functionof the fill factor of the array, the viscosity of the monomer solution,and the speed with which the substrate is withdrawn. At very large fillfactors, no conjoined microlenses are produced even at high withdrawalspeeds. As the fill factor is increased (higher density of microlenses),conjoined microlenses begin to appear at high withdrawal speeds. Ifconjoined microlenses are produced at a given fill factor, then for agiven withdrawal speed, more viscous monomers result in more of thesedefects than low viscosity monomers. Misshapen or missing microlensesalso occur. These defects can be minimized by using a monomer with asurface tension that is small enough that the monomer fully wets thehydrophilic areas of the substrate.

[0161] Even arrays fabricated with no defects exhibit non-uniformities.These non-uniformities are in the form of microlens-to-microlensvariations in focal length, and are a function of the substratewithdrawal speed. At slow withdrawal speeds, the f^(#)s of themicrolenses at the left and right edges (but not the top and bottomedges) of an array of microlenses are increased well above the averagef^(#) of microlenses in the array. (Here, left, right, top, and bottomare defined in relation to how the array is withdrawn from the monomersolution. The “top” edge of the microlens array is the edge that is“uncovered” first as the substrate is withdrawn). These edge effects areshown in FIG. 6. At fast withdrawal speeds, non-uniformities also occur.In this case, microlenses in the middle of the array have f^(#)s thatdeviate a great deal from the average value. An optimum withdrawal speedbetween these two extremes exists at which the uniformity of an array ofmicrolenses is maximized. In FIG. 7, the normalized variation in thefocal length, Δf/f, for a row of fifteen 500 μm-diameter microlenses(fabricated with a single dip-coat) is plotted as a function of thesubstrate withdrawal speed for two monomer solutions. The more viscousmonomer solution (Sartomer CD541), has a viscosity, μ, of ˜440 cP, andan optimum withdrawal speed of ˜400 μm/s. The medium-viscosity monomersolution (Ciba 5180, μ˜200 cP), has an optimum withdrawal speed of ˜1200μm/s. At these optimums, microlens arrays made with both of thesemonomers had a uniformity of Δf/f˜3.8%, corresponding to sag-heightvariations within the array of Δh/h<±2.5%. These values are competitivewith leading microlens fabrication technologies. [In using the resistreflow process, there is a great deal of variability in the sag-heightuniformity that can be achieved. Factors that affect the achievableuniformity include the microlens pitch, sag height, fill factor andmicrolens size. Typical sag height variations range from Δh/h˜±2%−±10%per Mr. John Rauseo, MEMS Optical Inc., 205 Import Circle, Huntsville,Ala. 35806 USA, in a personal communication to the inventors dated Dec.13, 2000.]

[0162] The uniformity of microlens arrays fabricated with multipledip-coats is also improved by withdrawing the substrate at an optimumspeed. Using the Sartomer CD541 monomer solution and withdrawing thesubstrate at the optimum withdrawal speed of ˜400 μm/s, an array of 500μm-diameter f/1.38 microlenses was fabricated using multiple dip-coatswith a uniformity of Δf/f˜±5.9% (Δh/h<±4.5%).

[0163] The reproducibility of the microlens fabrication process wascharacterized. Five small-fill-factor (hydrophilic:hydrophobic arearatio of 0.25) microlens arrays containing 500 μm diameter microlenseswere fabricated using a single 0-degree-tilt dip-coat in thehigh-viscosity monomer (Sartomer CD541, μ˜440 cP). The substrates werewithdrawn at the optimum withdrawal speed of ˜400 μm/s. The averagef^(#) of microlenses in these five arrays varied from a minimum of 3.88to a maximum of 4.02. Thus, the average f^(#) of an array of microlenseswas reproducible to within (4.02-3.88)/3.95˜3.5%. The apparatus used towithdraw substrates from the monomer solution did not allow strictcontrol of substrate-withdrawal-angle; with better control,reproducibility may possibly be improved.

[0164] In addition to the microlens focal length, array uniformity, andreproducibility, there are other microlens characteristics that are ofinterest, including the microlens diameter, the microlens surface shape(spherical vs. aspherical), the roughness of the microlens, and theaberrations that result. These characteristics are largely independentof the fluid transfer process.

[0165] The microlens diameter is defined only by the size of thehydrophilic domains patterned within the hydrophobic background. Thewithdrawal speed, tilt angle, array fill factor, monomer viscosity andmonomer surface tension affect the amount of monomer deposited duringfabrication, but not the size of the microlens footprint. Even multipledip-coats do not affect the microlens diameter; additional monomerassembles only on the existing cured microlens, a fact that was verifiedusing both optical and atomic force microscopy.

[0166] The general shape and surface roughness of microlenses formedwith our technique are also independent of the fluid transfer process.As the monomer assembles on the hydrophilic domains, it forms smooth,spherical caps under the influence of surface tension, regardless of thechoice of monomer solution, the withdrawal technique, and the number ofdip-coats used. The caveat is that the microlens must remain small(<˜1000 μm in diameter) so that gravity does not influence the shape ofthe resulting microlens. FIG. 8 shows optical and atomic forcemicroscope pictures of typical 50 μm diameter microlenses formed withsingle and multiple dip coats using our fabrication process. It can beseen that the surface profiles of the microlenses are quite smooth.Optical profiles (not shown) of such microlenses indicate that theydeviate from spherical by just ±5 nm for single-dip microlenses and by<±15 nm for multiple-dip microlenses.

[0167] Because the microlenses formed with this technique have excellentsurface profiles, with small deviations from spherical and very littlesurface roughness, aspherical aberrations will be minimized. Also, sincemost of the potential applications for microlenses involve only on-axisimaging, only spherical and chromatic aberrations will generally beimportant. Chromatic aberrations can be eliminated through properselection of a monomer with an index of refraction that is wavelengthinsensitive over the range of interest. Thus, only spherical aberrationis of particular concern. Computer simulations, conducted with Code Vsoftware (available from Optical Research Associates, Pasadena, Calif.,USA) were used to determine the point-spread function encircling 84% ofthe focused energy for various microlenses. The point-spread functionwas shown to range from ˜8.2 μm for f/4 microlenses to ˜47 μm for f/1.38microlenses. These values correspond to approximately 2x and 28x thediffraction-limited size of the central Airy disk. If such aberrationscannot be tolerated, input apertures could be fabricated to eliminatenon-paraxial rays.

[0168] 1.2. Theoretical Modeling of the Microlens Formation Method

[0169] 1.2.1 Background

[0170] In order to understand the trends that have been observedexperimentally, it is necessary to consider the process by which fluidis transferred to the hydrophilic domains of a heterogeneously-wettablesubstrate as it is withdrawn from a liquid bath.

[0171] Schwartz, et al., have considered the movement of a liquid layerover a heterogeneous substrate, comprised of a regular “patches” of lowenergy (hydrophobic) material within a background of high-energy(hydrophilic) material. See L. Schwartz, “Hysteretic Effects in DropletMotions on Heterogeneous Substrates: Direct Numerical Simulation”,Langmuir 14, 3440-3453 (1998); also Schwartz, R. Eley, “Simulation ofDroplet Motion on Low-Energy and Heterogeneous Surfaces”, Journal ofColloid and Interface Science 202, 173-188 (1998).

[0172] Numerical methods were used to solve the Navier Stokes equations(momentum conservation for fluids) for the speed, u(x,y,t) or height,h(x,y,t), of the liquid layer, at a given location and time on thesubstrate. The drawback of this approach is that because there is noanalytical solution for these functions, a qualitative assessment of thefactors that affect them is not (presently) possible. An alternativeapproach is to separately consider liquid flow on homogeneoushydrophilic and hydrophobic plates and then merge these results toobtain an approximate analytic solution for fluid flow on aheterogeneous substrate. This is the approach adopted in thisspecification.

[0173] As a clean homogeneous plate is withdrawn from an(uncontaminated) liquid bath, the solid-liquid interaction ischaracterized by a spreading coefficient, given by Equation 1:

S _(SL)=σ_(SV)−σ_(SL)−σ_(LV)  Equation 1

[0174] See Modern Approaches to Wettability: Theory and Applications, M.Schrader, G. Loeb, editors, (Plenum Press, New York, 1992). Here the σsrepresent the interfacial free energies per unit area (surface freeenergies) of the solid-vapor, solid-liquid, and liquid-vapor interfaces.The liquid-vapor surface free energy is also referred to as the liquidsurface tension. The plate will be wet by the liquid if the spreadingcoefficient is positive, and for the purposes of this specification thiswill be considered the criterion for a hydrophilic substrate.Conversely, a substrate will be hydrophobic if the spreading coefficientis negative.

[0175] The dip-coating of a homogeneous hydrophilic substrate, withdrawnvertically from a flat pool of an incompressible Newtonian fluid at acontrolled speed, will result in the accumulation of a liquid layer onthe hydrophilic surface. The thickness of this film of liquid was firstapproximated by Landau and Levich. See Landau and Levich, “Dragging of aLiquid by a Moving Plate”, Acta Physicochimica U.R.S.S. 17, 43-54(1942). The thickness of this film of liquid is given by Equation 2:$\begin{matrix}{t = {{0.946\quad \frac{\left( {\mu \quad U} \right)^{2/3}}{\left( {\rho \quad g} \right)^{1/2}}\left( \frac{1}{\sigma_{LV}} \right)^{1/6}} = {0.643\quad \left( \frac{3\mu \quad U}{\sigma_{LV}} \right)^{2/3}(R)}}} & \text{Equation~~2}\end{matrix}$

[0176] Here μ, ρ, and σ_(LV) are the liquid viscosity, density, andsurface tension respectively, g is the acceleration due to gravity, andU is the speed of substrate withdrawal. R is the radius of curvature ofthe static-meniscus region, which can be shown to be equal to(σ_(LV)/2ρg)^(½). See Landau and Levich, supra.

[0177] In contrast, a hydrophobic plate withdrawn from a solution willnot accumulate a liquid layer on its surface. Rather, the liquid willslip down the substrate. The slip speed, u, between the liquid andsubstrate at the liquid/substrate interface, is often assumed to bedirectly proportional to the sheer rate via a slip-length-that is:u=λ(∂u/∂y) where λ is the slip length, and y is the distanceperpendicular to the substrate surface. See L. M. Hocking, “Sliding andSpreading of Thin Two-Dimensional Drops”, Quarterly Journal of Mechanicsand Applied Mathematics 34, 37-55 (1981). See also P. Thompson, and S.Troian, “A general boundary condition for liquid flow at solidsurfaces”, Nature 389, 360-362 (1997).

[0178] With this assumption, and with the additional assumptions thatthe slip speed is small and that the force of gravity is small comparedto the liquid surface tension, the maximum speed with which a twodimensional liquid drop having lateral dimension a₀ will slip down ahydrophobic substrate is given by: $\begin{matrix}{u = \frac{\left( {a_{0}\Theta_{0}} \right)^{2}\rho \quad g}{\mu \quad {\log \left( \frac{2a_{0}\Theta_{0}}{3\lambda} \right)}}} & \text{Equation~~3}\end{matrix}$

[0179] Here, u is the maximum speed with which the drop slips, andshould not be confused with the substrate withdrawal speed, U. Thedensity and viscosity of the liquid are represented by ρ and μrespectively, and g is the acceleration due to gravity. See L. M.Hocking, supra. The slip length, λ, can be made large by making σ_(SL)small (i.e. by making the substrate more hydrophobic). See P. Thompsonand S. Troian, supra. See also B. Jean-Louis, “Large Slip Effect at aNonwetting Fluid-Solid Interface”, Physical Review Letters 82, 4671-4674(1999).

[0180] θo is the contact angle of the liquid drop resting on thehydrophobic surface, and is given by the following equation 4:$\begin{matrix}{{\cos \quad \Theta_{0}} = \frac{\sigma_{SV} - \sigma_{SL} + \left( \frac{\tau}{r} \right)}{\sigma_{LV}}} & \text{Equation~~4}\end{matrix}$

[0181] where σ_(LV), σ_(SV), and σ_(SL) are the surface-free energies(or equivalently, surface tensions) of the liquid-vapor,substrate-vapor, and substrate-liquid interfaces, respectively. ‘T’ isthe “line tension” of the three-phase contact line, where the solid,liquid, and vapor phases meet, and ‘r’ is the radius of the base of thedrop. See B. Widom, “Line Tension and the Shape of a Sessile Drop”, J.Phys. Chem. 99, 2803-2806 (1995). In general, for small volumes ofliquid, the line-tension can have a profound effect upon the equilibriumcontact angle. See B. Widom, supra. However for the liquid volumes andmonomer surface tensions that we utilized in our experiments, theline-tension is small and may be ignored. Equation 4 then reduces to thewell-known Young-Dupre equation. See J. Pellicer, J. Manzanares, and S.Mafe, “The physical description of elementary surface phenomena:Thermodynamics versus mechanics”, Am. J. Physics 63, 542-547 (1995); andF. Behroozi, H. Macomber, J. Dostal, C. Behroozi, and B. Lambert, “TheProfile of a Dew Drop”, Am. J. Phys. 64, 1120-1125 (1996).

[0182] From this equation 4, it is evident that the contact angle at theliquid-solid interface can be increased by decreasing σ_(SV), (i.e.making the substrate more hydrophobic), or by increasing σ_(LV) (i.e.increasing the liquid-air surface tension).

[0183] The speed, u, given by Equation 3 represents the speed with whichan isolated liquid drop, having a constant volume (with lateraldimension a_(o)), will slip down a uniform hydrophobic substrate. It isnot directly applicable to a dip-coating process in which the volume ofliquid pulled up from the bath is a dynamic quantity. Nonetheless,Equation 3 is useful in describing the general trends exhibited in thedip-coating of hydrophobic substrates.

[0184] 1.2.2 Heterogeneous Plate

[0185] Liquid draining from the hydrophobic areas of a heterogeneoussubstrate will follow the same trends as liquid draining from a purelyhydrophobic substrate. i.e. the trends will be given by Equation 3. Forinstance, an increase in the monomer contact angle, or a decrease inmonomer viscosity will result in an increased drain speed.

[0186] However on a heterogeneous substrate, hydrophilic domains alsoexist that will slow the draining liquid as it rolls off the substrate,and the distribution of these hydrophilic domains will affect how themonomer drains. Monomer solution draining from the middle of an array ofhydrophilic domains will “feel” more hydrophilic material, and drainslower than will monomer solution draining at the left and right arrayedges, where a purely hydrophobic environment exists to one side. At thecenter of the array, where the drain speed reaches a minimum, the drainspeed is denoted U0 _(drain), and is a function of the amount ofhydrophilic material that exists (i.e. the array fill factor). At theleft and right edges of the array the drain speed will attain a maximumvalue of UE_(drain). This maximum value of the drain speed isessentially the same as the drain speed of a liquid on a purelyhydrophobic substrate, and follows the trends of Equation 3.

[0187] Although it is not explicitly indicated, it should be rememberedthat U0 _(drain) is a function of the array fill factor, and that bothU0 _(drain) and UE_(drain) are functions of the monomer viscosity andsurface tension (Equation 3 and Equation 4). Thus, the value of U0_(drain) is specific to a given array fill factor, and both U0 _(drain)and UE_(drain) are specific to a given monomer solution.

[0188] For a given array fill factor and monomer solution, if thesubstrate is withdrawn at a speed that is less than or equal to U0_(drain), then the withdrawal speed and drain speed will be one and thesame. On the other hand, if the substrate withdrawal speed is equal toor greater than the maximum drain speed of the liquid, UE_(drain), thenthe liquid will drain at a rate given roughly by Equation 3, independentof further increases in the substrate withdrawal speed. These twopossibilities define two different regimes for the heterogeneous plate,and it is predicted that very different trends will be observed in thesetwo regimes.

[0189] In the first regime, the substrate is withdrawn at a speed thatis less than or equal to U0 _(drain). The withdrawal speed is thereforethe same as the drain speed. In this regime, the amount of liquid thatis deposited on the hydrophilic domains will follow the trends given byEquation 2. Specifically, increasing monomer viscosity or substratewithdrawal speed, or decreasing monomer surface tension will give riseto an increase in the sheer force exerted on the monomer solution, whichin turn will cause more solution to remain on the substrate.

[0190] In the second regime, the substrate is withdrawn at a speed thatis equal to or greater than UE_(drain). Increasing the substratewithdrawal speed further will not have an affect on this drain speed—theliquid will drain at a maximum speed, UE_(drain), given roughly byEquation 3, regardless of how fast the substrate is withdrawn. Theliquid layer thickness that can be deposited at this maximum drain speedcan be found by inserting Equation 3 into Equation 2. The followingexpression (Equation 5) results: $\begin{matrix}{\left. \tau \right.\sim\frac{\left( {a_{0}\Theta_{0}} \right)^{4/3}\left( \frac{\rho \quad g}{\sigma} \right)^{1/6}}{\left\lbrack {\log \left( \frac{2\quad a_{0}\Theta_{0}}{3\lambda} \right)} \right\rbrack^{2/3}}} & \text{Equation~~5}\end{matrix}$

[0191] Here, t is the thickness of the liquid adhering to thehydrophilic domains, and all other parameters have been previouslydefined.

[0192] Equation 5 shows that, as expected at the maximum drain speed,the thickness of the liquid layer on the hydrophilic domains isindependent of further increases in substrate withdrawal speed. Fromthis equation 5 it can also be observed that at this maximum drainspeed, the liquid layer thickness will no longer be influenced by theliquid viscosity. This can be understood because as the monomerviscosity increases, the sheer force at any given withdrawal speedincreases, (Equation 2), but the maximum drain speed, UE_(drain),decreases (Equation 3), and these two effects tend to cancel. Equation 5also predicts, however, that the contact angle (partially determined bythe surface tension of the monomer), and the slip coefficient (partiallydetermined by the surface tension of the solid/liquid interface) willgovern the liquid thickness that can be achieved.

[0193] 1.3 Comparison of Theory with Reality

[0194] As predicted by theory, liquid draining from the heterogeneoussubstrate followed trends given by Equation 3. Increases in the monomercontact angle (surface tension), and decreases in monomer viscosityresulted in increased drain speeds. See Table 1.

[0195] The amount of liquid that is deposited on each hydrophilic domainis directly related to the f^(#) of the resulting microlens; moremonomer deposition results in a stronger (lower f^(#)) microlens. Thus,in regime 1, in which liquid deposition is governed by Equation 2 it ispredicted that as the withdrawal speed is increased from zero, themicrolens f^(#) will start off very large, and get progressively smalleras the withdrawal speed is increased up to U0 _(drain). In this regime,it is also predicted that for a given withdrawal speed, monomers withlarge viscosities and small surface tensions will result in stronger(lower f^(#)) microlenses. These are precisely the trends that wereobserved experimentally in the graph of f^(#) vs. withdrawal speed (FIG.2).

[0196] As the withdrawal speed is increased further, past UE_(drain),theory predicts the beginning of regime 2. In this regime, the microlensf^(#) will be minimized at a constant value, independent of furtherincreases in withdrawal speed (Equation 5). Equation 5 further predictsthat the minimum achievable f^(#) should be independent of viscosity buthighly dependent on monomer surface tension.

[0197] By experimental observation it was found that the minimum f^(#)occurred at a withdrawal speed of U0 _(drain) and increased slightlybefore becoming constant at higher speeds. This surprising result can beunderstood because the value of U0 _(drain) is actually a dynamicquantity. If the substrate is withdrawn at a speed≦U0 _(drain), thesurface tension of the monomer pool exerts a pull on the drainingmonomer that slightly increases the value of U0 _(drain). On the otherhand, if the substrate is withdrawn at a speed>U0 _(drain), the drainingliquid is further removed from the surface of the monomer pool and thevalue of U0 _(drain) is reduced. Thus, the average f^(#) of formedmicrolenses is minimized at a withdrawal speed of U0 _(drain) becausethis is the fastest speed with which monomer can drain. This was notpredicted by theory because the equations we used were for isolatedliquid drops, and the effect of the monomer pool was therefore notconsidered theoretically. At withdrawal speeds>U0 _(drain), however, thef^(#) of formed microlenses does become constant (FIG. 2, SartomerCD541), in agreement with theoretical predictions.

[0198] Experimentally, it was found that the minimum achievable f^(#)could be made smaller by increasing monomer viscosity or surface tension(Table 1). However from Table 1 it can also be seen that the minimumf^(#) was far more sensitive to changes in surface tension than inviscosity. For instance the Sartomer SR601 monomer solution has aviscosity that is more than double that of the Sartomer CD541 solution,but approximately the same surface tension. The additional liquid layerthickness deposited by the more viscous monomer is small (4 μm). On theother hand, the glycerol/water solution has a viscosity very similar tothe Sartomer CD541 solution, but almost double the surface tension. Theadditional layer thickness deposited by the glycerol/water solution islarge (11 μm). Thus, the experimental results differ from theory in thatviscosity does affect the minimum achievable f^(#). However the relativeinsensitivity of the minimum f^(#) to changes in viscosity compared tochanges in surface tension is in keeping with theoretical predictions.

[0199] Equation 2 and Equation 5 implicitly indicate that the f^(#) offormed microlenses will be a function of the microlens array fillfactor. This is because, as discussed, arrays with high fill factorswill have a smaller U0 _(drain) than arrays with low fill factors. Atwithdrawal speeds greater than U0 _(drain) (when arrays of all fillfactors are in regime 2) the average f^(#) of microlenses formed on highfill factor arrays will therefore become constant at a larger value (themicrolenses will be weaker) than arrays with low fill factors. Thistrend can be seen in the experimental results of FIG. 4 in which lowfill-factor arrays clearly give rise to microlenses with lower f^(#)s athigh speeds. However FIG. 4 also shows the at low withdrawal speeds,less than U0 _(drain), the same trends exist. This is not explained bythe model, which predicts that the f^(#)s of microlenses formed atspeeds less U0 _(drain) should be independent of fill factor. Theexplanation for this discrepancy is that as the monomer solution rollsoff the hydrophobic areas of the substrate, it must either drain fromthe substrate, or “snap back” onto the hydrophilic domains. Monomersolution draining from arrays with large fill-factors does not snapback, but instead drains towards the adjacent (close) row of hydrophilicdomains. In contrast, more monomer solution accumulates on thehydrophilic domains of arrays with small fill-factors, resulting instronger (lower f^(#)) microlenses even at low withdrawal speeds.

[0200] The equations for liquid layer thickness (Equation 2 and Equation5) do not contain any terms that constrain the size of the hydrophilicdomains. It is therefore predicted that for a given microlens shape(e.g. circle, square, etc.), increasing the size of the microlens shouldnot appreciably affect the microlens the f^(#) provided that the fillfactor of the array is maintained constant. This prediction wasconfirmed experimentally by the relative insensitivity of f^(#) withmicrolens diameter (FIG. 5).

[0201] Finally, the f^(#) of formed microlenses will also depend on thesubstrate dipping angle due to the affect that the dipping angle has onthe shape of the static meniscus. If the substrate is tilted at anangle, the radius of curvature of the static meniscus on the top side ofthe plate is made larger, while the radius of curvature of the staticmeniscus on the bottom-side of the plate becomes smaller. From Equation2 it can be seen that these changes in the radius of curvature of thestatic meniscus will cause a thicker liquid layer to be deposited on thetop side, while reducing the thickness of the deposited layer on thebottom side. Thus it is expected that if the patterned side of thesubstrate is tilted up, stronger (lower f^(#) microlenses) will result.This prediction was confirmed experimentally.

[0202] Two factors will influence the achievable uniformity of themicrolens arrays. First and foremost, of these factors is the shape ofthe three-phase (solid-liquid-air) contact line as it rolls off thesubstrate. At the left and right edges of an array of hydrophilicdomains there will exist an asymmetrical distribution of hydrophilicarea, and the three-phase contact line will be deformed (FIG. 9). Moremonomer solution will drain from the substrate at these edges, leadingto a decrease in liquid volume remaining on the hydrophilic spots, and acorresponding increase in the f^(#) of microlenses at the left and rightedges. These predicted edge effects are in accordance with theexperimental results of FIG. 6, though it was found that they occurredpreferentially at low withdrawal speeds. One possible reason why edgeeffects tend not to occur at high speeds is that at high speeds thethree-phase contact line does not have time to deform to the extent thatit does at low withdrawal speeds.

[0203] The shape of the three-phase contact line will also affect theuniformity of the central part of microlens arrays (away from the leftand right edges). If the substrate is withdrawn from the monomersolution at a speed no greater than U0 _(drain) (regime 1) then astraight solid-liquid-air contact line will be preserved across theentire substrate (except at the edges), and the monomer will drainsmoothly, generating a uniform microlens array. On the other hand, ifthe substrate is withdrawn at a speed greater than U0 _(drain), thethree-phase contact line will be deformed, and monomer will drainnon-uniformly, leading to non-uniformities in the f^(#)s of themicrolenses that result.

[0204] The second factor that will contribute to array non-uniformitywill be that at low speeds, a relatively small amount of monomersolution will be deposited in each hydrophilic domain. Because themicrolenses thus formed have a small volume, they will be quitesensitive; small microlens-to-microlens volume differences willinfluence their focal length significantly, resulting in a microlensarray that is more non-uniform than one fabricated at a higher speed.

[0205] On the basis of this discussion, the existence of an optimumwithdrawal speed, at which the standard deviation of the focal length ofmicrolenses in an array is minimized is predicted. This optimum wasexperimentally verified, and shown to occur at a withdrawal speed U0_(drain). At this speed, the microlens volume is maximized, and themonomer drains as smoothly as possible from the substrate.

[0206] On the basis of our experiments and our theoretical analysis, wesummarize the requirements which allow the manufacturing ofhigh-performance (i.e. low f^(#)), uniform and reproducible microlensarrays utilizing the hydrophobic effect:

[0207] 1) To produce single-dip low f^(#) microlenses:

[0208] a) The substrate withdrawal speed should be made equal to U0_(drain). Increasing the substrate withdrawal speed further will resultin a slight increase in f^(#).

[0209] b) A large drain speed, U0 _(drain), is desired. To maximize thedrain speed:

[0210] i) A large liquid-solid contact angle is desirable on thehydrophobic regions of the substrate. This can be achieved by decreasingthe energy of these regions (by using a more hydrophobic adhesivelayer), or by increasing the monomer surface tension.

[0211] ii) A large slip coefficient, λ, is desired. λ can be made largeby minimizing the substrate-liquid interface energy (by using a morehydrophobic adhesive layer).

[0212] c) A viscosity greater than or equal to ˜200 cP is desired.Theoretically, at speeds equal to or greater than UE_(drain), the layerthickness (and hence the resulting microlens f^(#)) should not depend onviscosity. Experiments show however that a viscosity of ˜200 cP orgreater is needed to minimize f^(#).

[0213] 2) To maximize uniformity:

[0214] a) To prevent severe defects, hydrophilic and hydrophobic regionsof the substrate must have positive and negative spreading coefficients,respectively (Equation 1).

[0215] b) The number of conjoined microlenses can be reduced by makingthe fill factor of the array smaller. If this is not an option,withdrawal speed and/or monomer viscosity must be reduced.

[0216] c) Assuming a small enough fill factor that conjoined microlensesare not generated, substrates should be withdrawn at U0 _(drain), themaximum speed with which liquid can drain from the central portion ofthe array, while still preserving a uniform three-phase contact line.

[0217] d) Extra “dummy” microlenses should be fabricated to the left andright sides of an array so that edge effects can be ignored. This isparticularly important in high-fill-factor arrays, where the withdrawalspeed must be kept small (<U0 _(drain)) to avoid production of defects.

[0218] 3) For best reproducibility, careful control of substrate dippingangle is required.

[0219] 1.4 Summary of Basic Microlens Fabrication Method of the PresentInvention

[0220] In summary, the performance of polymer microlens arraysfabricated by dip-coating patterned hydrophilic/phobic substrates wasquantitatively analyzed and optimized. At low withdrawal speeds theaverage f^(#) of formed microlenses could be reduced by increasingsubstrate withdrawal speed or monomer viscosity, or by decreasingmonomer surface tension. At larger withdrawal speeds, the average f^(#)was minimized and become constant, independent of withdrawal speed. Theminimum f^(#) was achieved at a withdrawal speed U0 _(drain)corresponding to the maximum speed with which monomer solution can drainsmoothly from the substrate while still preserving a straightliquid-air-solid contact line. The minimum achievable f^(#) could bereduced by using a monomer with a large viscosity and large surfacetension. At all withdrawal speeds, the f^(#)s of formed microlensescould be reduced by decreasing the array fill factor or by tilting thesubstrate so that its patterned side was tilted up during the withdrawalprocess. Dynamic control of the withdrawal speed allowed microlenseshaving the same diameter but different f^(#)s to be fabricated withinthe same array. Uniformity of microlens arrays was analyzed with an eyeto both reducing defect density and minimizing microlens-to-microlensvariations in arrays. The number of conjoined microlenses was reduced bymaking fill factors sufficiently small, or by reducing the monomerviscosity or withdrawal speed. The number of missing and misshapenmicrolenses was reduced by ensuring that the monomer surface tension wassmall enough that the monomer fully wet the hydrophilic domains. Inmicrolens arrays in which defects were not a problem, U0 _(drain), wasshown to be the optimum withdrawal speed at which array uniformity wasmaximized. At this optimum, arrays of f/3.48 microlenses were fabricatedusing one dip-coat with uniformity better than Δf/f˜±3.8%. Multipledip-coats allowed production of arrays of f/1.38 microlenses with,uniformity better than Δf/f˜±5.9%. Average f^(#)s were reproducible towithin 3.5%. Other microlens characteristics such as the diameter,shape, and surface roughness of the microlenses were shown to beexcellent, and independent of the fluid transfer process. A model wasdeveloped to describe the fluid transfer process by which monomersolution forms microlenses on the hydrophilic domains. Good agreementbetween theory and experimental results was found.

[0221] The technique we have developed for the fabrication ofmicrolenses offers several advantages over more conventional methods(resist-reflow, ink-jet, etc.). First, it is extremely low-cost,requiring only a mask, and a UV source for the lithographic exposures.Since there is only one masking step, there is no need for an expensivemask aligner. Second, all processing may be performed at roomtemperature, allowing integration of microlenses with temperaturesensitive materials and components. Third, the polymer microlenses aredirectly fabricated from robust, optically-transparent polymers,eliminating the need for an etch transfer step (though such etchtransfers may be performed if desired). Finally, our process appears tobe competitive with other technologies in offeringlithographic-alignment, low-f^(#)s, large fill-factors, sphericalsurface profiles, and excellent array uniformity and reproducibility.There are, of course, limitations in the technique. For instance, somesubstrate-liquid systems do not meet the criteria of Equation 1, andsuch systems are unsuitable for microlens fabrication. Also, thefabrication of uniform high-fill-factor arrays can be tricky, since itis often necessary to withdraw such substrates below the optimum speedto ensure defect-free arrays. Nonetheless, we feel that for manyapplications our technique is competitive and in some cases superior toexisting microlens fabrication technologies.

[0222] 2. Fabricating Microlenses in Self-Alignment to OpticalComponents

[0223] An extension and adaptation of the microlens fabrication methodof the present invention permits the ready fabricating microlenses whichare self-aligned to optical fibers and low-wavelength (<500 nm)single-mode light output devices. Unlike most integration techniques,our fabrication method allows the production of self-aligned microlensesboth directly on optical components and removed from these components bya spacer. This later capability is, to the best knowledge of theinventors, unique.

[0224] Additionally, the extended fabrication method of the presentinvention requires very little equipment, no heat, and only an optionaletch-transfer step over the basic method, making our integration methodextremely low-cost. Microlenses integrated with fibers haveoptical-quality smooth surfaces, deviating from spherical by just ±15 nmover their centers. These microlenses have f^(#)s as low as 1.55 and,because they are self-aligned, can be integrated in optical systems thatrequire alignment tolerances that would be impractical using any othertechnique (known to the inventors). As just previously stated,two-dimensional arrays of such microlenses can be made with excellentuniformity (Δf/f˜5.9% for a 15×15 array of 500 μm f/1.4 microlenses),stability, and reproducibility (average f^(#)s are reproducible towithin 3.5%).

[0225]FIG. 10, consisting of FIGS. 10a through 10 f, diagrammaticallyillustrates our extended method of the present invention for thefabrication of a single microlens self-aligned to an optical fiber on aglass spacer. First, an adhesive hydrophobic layer is mechanicallyapplied to a transparent substrate, and photoresist is spun over thislayer. Next, the substrate is glued perpendicularly to the end of anoptical fiber using an optically transparent adhesive. After theadhesive dries, light is shined through the optical fiber, exposing thephotoresist only at the fiber output. The hydrophobic layer is nowetched away from the exposed region, using an O₂ plasma etch, and theremaining photoresist is then stripped, leaving a hydrophilic domainpatterned just above the fiber output in a hydrophobic background. Ifthe substrate is then dipped into and withdrawn from aUV-curable-monomer solution, the monomer will self-assemble into amicrolens on the hydrophilic domain. After a UV-cure the microlensbecomes hard and stable. After curing, if a stronger (lower f^(#))microlens is desired, the substrate may be re-dipped into the monomersolution. Additional monomer solution assembles on top of the existingcured microlens, causing an increase in the radius of curvature, and acorresponding reduction in f^(#). This process of curing and re-dippingmay be used repeatedly to reduce the f^(#) of the fabricated microlens.The technique for integrating microlenses directly on fibers (with nospacer) is much the same. The fiber end is mechanically coated with ahydrophobic material, and photoresist is then simply dabbed (not spun)over this hydrophobic layer. The remainder of the procedure is asdescribed above. Although dabbing the photoresist onto the fiber givesrise to a non uniform resist layer, high quality microlenslets cannonetheless be formed with this technique.

[0226] Commercial high-wavelength photoresists are designed for optimumexposure at wavelengths<500 nm. On the other hand, optical fibers forcommunication are designed to carry higher wavelengths (850, 1310, and1550 nm). This difference has two important implications in ourprocedure. First, it means that during the microlens-writing process,there will be significant optical power loss as the light propagatesthrough the fiber. To address this concern a more intense writing lightcan be used, or short optical fibers can be used during the writeprocess, and then spliced to longer fibers after the microlenses areformed. The second problem is that at short wavelengths, opticalcommunication fibers support multiple modes. If coherent laser lightfrom (for example) and Ar source (λ=488 nm) is used to expose the resistthrough the fiber, non-circular mode patterns are formed in the resist.Microlenses formed from such footprints are highly aberrated. Thesolution to this problem is to couple white light into the fiber duringthe exposure. The white light produces a very large number of modes inthe fiber, resulting in the “smearing” of mode patterns, and thegeneration of a circular footprint in the resist.

[0227] It is generally desirable to fabricate a microlens with adiameter that is larger than the output beam size (i.e., larger than the1/exp² beam diameter). This can be achieved by writing the microlenswith a beam intensity that is greater than the desired operatingintensity. During the writing process the beam diameter will be largeand will generate a large microlens footprint. During operation the beamdiameter will be smaller, and will under-fill the microlens so that themicrolens captures a maximum amount of the beam power.

[0228] The precise diameter of the exposed-footprint depends on a numberof factors, including the intensity and wavelength content of theillumination light being used, the fiber core size, the spacer size, thesensitivity of the particular photoresist used, and the exposure time. Avery good estimation, however, can be obtained from a knowledge of thenumerical aperture of the fiber. The diameter of the exposed footprintis approximated by Equation 6: $\begin{matrix}{D = {d + {2\left( \frac{l}{n} \right)\quad {\tan \left( {{SIN}^{- 1}\left( {N.A.} \right)} \right)}}}} & \text{Equation~~6}\end{matrix}$

[0229] Here D is the size of the exposed footprint, d is the corediameter, 1 is the glass spacer thickness (the distance between theoutput of the fiber and the resist layer), n is the index of refractionof the glass spacer, and N.A. is the numerical aperture of the fiber.

[0230] In our experiments we used Corning Single Mode Optical Fiber SMF28. The core diameter of this fiber is ˜10 μm, and the numericalaperture is constant at about 0.14 over a wide wavelength range. (TheN.A. of Corning Single Mode Optical Fiber SMF 28 is approximatelyconstant from 500 nm-1300 nm. per a personal communication to theinventors of Nov. 24, 2000 from Corning, Inc., TelecommunicationsProducts Division Technical Support, Corning, N.Y. 14831 USA.) Usingglass microscope slides (1=1000 μm, n=1.5), we calculate a theoreticaldiameter for the footprint of the microlens of 198 μm.

[0231] Experimentally, we found that resist holes varied in sizesomewhat depending upon the intensity and length of the exposure. Thesize range of formed resist holes, however, was 175-200 μm in diameter,in good agreement with theoretical predictions. FIG. 11a shows a 175 μmdiameter photoresist hole formed using the described conditions. Thispicture was taken at an angle so that the V-groove where the opticalfiber rests and the photoresist hole are both visible. However theresist hole is perfectly self-aligned to the output of the opticalfiber.

[0232] After O₂ plasma etching the substrate and then stripping theresist, the substrate was dipped into a polymer solution, allowing theformation of a microlens in the precise location where the resist holewas fabricated. This microlens is shown in FIG. 11b, and again (athigher magnification), in FIG. 11c. The microlens shown here was dippedand UV-cured multiple times in order to produce a strong (f/1.55)microlens.

[0233] It can be seen that the microlens appears quite circular, thoughthere are a few “spurs” on its circumference. Careful attention to indexmatching at the interfaces, perfectly-perpendicular alignment of thefiber at the fiber-spacer interface, and proper choice of photoresistand spacer materials may eliminate such non-uniformities. In any case,these spurs do not greatly affect the performance of the microlens. Thesurface profile of this particular microlens, for instance, was measuredusing optical interferometric techniques, and the microlens was found todeviate from spherical by just ±15 nm over its center (FIG. 12).

[0234] It is easy to extend this technique to the parallel fabricationof multiple self-aligned microlenses in two dimensional arrays. To dothis, it is only necessary that light be transmitted through each fiberin the array so that the resist is exposed at each fiber output. Thescheme for such a process uses a “writing array”, consisting of an arrayof optical fibers with fiber connectors (FCs) at their ends. Lightintensity at the output of each FC can be measured and adjustedappropriately. The fibers in the array of interest (on which we desireto fabricate microlenses) are now connected to the writing array withcomplementary FCs, and the exposure is allowed to occur. After theexposure, the array can be removed, a new array attached to the writingarray, and the process repeated. With the use of the writing-array, itis only necessary to adjust the beam intensities through each fiberonce. After this initial adjustment, identical arrays of microlenses canbe fabricated on many fiber arrays.

[0235] A unique aspect of this fabrication process is that the footprint(and hence the focal length) of each microlens at each fiber output inthe array can be tailored by careful selection of the intensity of lightthat is transmitted through each fiber during the writing process. Forexample, transmission of equal intensity light through each fiber willresult in a uniform array of microlenses with the same focal length. Onthe other hand, adjacent microlenses can be fabricated with verydifferent focal lengths, simply by transmitting different intensities oflight through each fiber.

[0236] In summary, the expanded method of the present invention showshow to fabricate microlenses that are fully-self-aligned to opticalfibers and low-wavelength (<500 nm) single-mode output devices. Themethod requires very little equipment, no alignment steps, and no heat.All of these factors contribute to making the method extremely low-cost.The method has been used to fabricate microlenses directly on the endsof optical fibers as well as on transparent spacers separated from thefibers. The microlenses so formed have excellent surfacecharacteristics, deviating from spherical by just ±15 nm, and can befabricated with f^(#)s as low as 1.55. Because the microlenses areself-aligned, low f^(#) microlenses can be integrated in optical systemsthat require alignment tolerances that would be impractical using anyother technique. It is a simple matter to extend this method to thefabrication of arrays of microlenses each self-aligned to an individualfiber in a massively parallel fashion. Accordingly, while the basemethod or the present invention teaches that a parallel scheme can beused to generate uniform, stable reproducible arrays of microlenses, theenhanced method teaches that it is also possible to fabricate in amassively parallel fashion great numbers of microlenses that aresel-aligned to correspondingly great numbers of optic fibers or lightsources. See also the inventors' own published papers: D. Hartmann, O.Kibar, and S. Esener, Optics Letters 25, 975, (2000); D. Hartmann, O.Kibar, and S. Esener, submitted to Applied Optics, (2000); and D.Hartmann, O. Kibar, and S. Esener, Optics in Computing, R. Lessard, T.Galstian, Ed., SPIE 4089, 496 (2000).

[0237] In accordance with the preceding explanation, variations andadaptations of the methods in accordance with the present invention willsuggest themselves to a practitioner of the optical and optical devicearts. For example, the monomer need not be cured with ultraviolet light,but may be cured by temperature, chemicals, or diverse other ways wellknown in the chemical arts.

[0238] As a more profound difference, it is known that conductivepolymers can be transparent, and that transparent polymers may beconductive—as may be verified by a search for both terms in the fulltext issued patents of the United States as are available at the website of the United States Patent and Trademark Office. It is thusperceived possible to produce on one substrate microlenses—primarily foroptical communication—and bump pads—primarily for electricalconnection—all at the same time by use of but one polymer precursorsolution in but one single, unified, process. The value of making bothelectrical and optical connections—especially as are both simultaneouslyself-aligned—in a single process is obvious.

[0239] In accordance with these and other possible variations andadaptations of the present invention, the scope of the invention shouldbe determined in accordance with the following claims, only, and notsolely in accordance with that embodiment within which the invention hasbeen taught.

What is claimed is:
 1. A method of fabricating a polymer microstructurecomprising: withdrawing a stable base of patterned wettability from aliquid polymer precursor; followed by solidifying the liquid polymerprecursor remaining on the stable base into a solid polymermicrostructure.
 2. The method of claim 1 adapted to the fabricating ofpolymer microlenses upon a substrate wherein the withdrawing is of asubstrate of patterned wettability from the liquid polymer precursor soas to leave in hydrophilic areas of the substrate caps of the liquidpolymer precursor which are subsequently solidified by curing so as toform solid polymer microlenses.
 3. The method of fabricating polymermicrolenses according to claim 2 wherein the withdrawing is adjustablycontrolled in at least one of (i)liquid viscosity, (ii) liquid surfacetension, (iii) liquid density, (iv) liquid index of refraction, (v) thesurface-free-energies of the hydrophilic and hydrophobic areas of thesubstrate (vi) the angle of substrate withdrawal, (vii) the speed of thesubstrate withdrawal, (viii) the proximity of hydrophilic areas to eachother, and (ix) the number of any times the withdrawing is repetitivelyperformed, so as to controllably fabricate a microlens with a desiredf-number (f^(#)).
 4. The method of fabricating polymer microlensesaccording to claim 2 wherein the withdrawal speed is varied specificallyso as to vary the f#s of polymer microlenses in different regions of thesubstrate.
 5. Polymer microlenses fabricated by the method of claim 2.6. The method of claim 1 adapted to the fabricating of a polymermicrolens upon an end of an optical fiber wherein the withdrawing is ofan optical fiber end of patterned wettability from the liquid polymerprecursor so as to leave in hydrophilic areas of the optical fiber end aspherical cap of the liquid polymer precursor which is subsequentlycured so as to form a solid polymer microlens.
 7. The method offabricating a microlens according to claim 6 wherein the withdrawing isadjustably controlled in at least one of (i) liquid viscosity, (ii)liquid surface tension, (iii) liquid density, (iv) liquid index ofrefraction, (v) the surface-free-energies of the hydrophilic andhydrophobic areas of the optical fiber end, (vi) the angle of opticalfiber end withdrawal, (vii) the speed of the optical fiber endwithdrawal, (viii) the proximity of any multiple hydrophilic areas toeach other, and (ix) the number of times the withdrawing is repetitivelyperformed, so as to controllably fabricate a microlens with a desiredf-number (f^(#)).
 8. A polymer microlens upon an optical fiberfabricated by the method of claim
 6. 9. A method of fabricating apolymer microstructure comprising: applying an adhesive hydrophobic orhydrophilic layer to a substrate; patterning the adhesive hydrophobic orhydrophilic layer upon the substrate so as to make aheterogeneously-wettable substrate with at least one region that ishydrophilic and at least one region that is hydrophobic; depositing aliquid polymer precursor on the at least one hydrophilic region of theheterogeneously-wettable substrate so as to form a polymermicrostructure adhering to the substrate.
 10. The method of fabricatinga polymer microstructure according to claim 9 further comprising: curingthe liquid polymer precursor remaining on the at least one hydrophilicregion of the substrate so as to form a polymer microstructure, adheringto the substrate, that is solid.
 11. The method according to claim 9wherein the applying of the hydrophilic or hydrophobic layer comprises:mechanical polishing.
 12. A polymer microstructure fabricated by themethod of claim
 9. 13. A method of fabricating a polymer microstructurecomprising: patterning an adhesive hydrophobic or hydrophilic layer upona substrate so as to make a heterogeneously-wettable substrate with atleast one region that is hydrophilic and at least one region that ishydrophobic; depositing a liquid polymer precursor on the at least onehydrophilic region of the heterogeneously-wettable substrate so as toform a polymer microstructure adhering to the substrate.
 14. The methodof fabricating a polymer microstructure according to claim 13 furthercomprising: curing the liquid polymer precursor remaining on the atleast one hydrophilic region of the substrate so as to form a solidmicrostructure adhering to the substrate.
 15. A polymer microstructurefabricated by the method of claim
 13. 16. A method of fabricating one ormore microlenses comprising: applying a hydrophobic layer to asubstrate; patterning the hydrophobic layer into one or more areas;dipping the substrate with its selectively patterned hydrophobic layerinto a liquid polymer precursor solution; and controllably withdrawingthe substrate from the solution so that, as the substrate is withdrawn,the liquid solution drains from the hydrophobic areas of the substratebut remains on the hydrophilic areas, the solution there forming inthese hydrophilic areas liquid caps under the influence of surfacetension, the precise volume of which is determined and controlled by inrespect of at least one of (i) liquid viscosity, (ii) liquid surfacetension, (iii) liquid density, (iv) the surface-free-energies of thehydrophilic and hydrophobic areas of the substrate (v) the angle ofsubstrate withdrawal, (vi) the speed of the substrate withdrawal, (vii)the proximity of hydrophilic areas to each other, and (viii) the numberof times the dip-coating process is performed; curing the remaining uponthe substrate so as to make one or more solid polymer microlenses. 17.The method according to claim 16 that after the curing furthercomprises: transferring the at least one microlens into the underlyingsubstrate by an etch transfer process.
 18. The method according to claim16 that, after the curing, further comprises: re-dipping the substratewith its at least one microlens into the liquid solution so thatadditional liquid assembles on top of the existing cured microlens;re-withdrawing the substrate from the liquid; and re-curing thenewly-added liquid present upon the at least one microlens that is uponthe substrate so as to make that this at least one microlens incurs adecrease in the radii of curvature, and a corresponding reduction inf^(#).
 19. The method according to claim 18 wherein the re-dipping, there-withdrawing and the re-curing are performed repeatedly so as toproduce at least one microlens having a desired low f^(#)).
 20. Themethod according to claim 16 that, after the curing, further comprises:condensing additional liquid polymer precursor on top of the existingcured at least one microlens; and re-curing the newly-added liquidpresent upon the at least one microlens that is upon the substrate sothat the at least one microlens incurs a decrease in the radii ofcurvature, and a corresponding reduction in f^(#).
 21. The methodaccording to claim 20 wherein the condensing of additional liquidpolymer precursor, and the re-curing, are performed repeatedly so as toproduce at least one microlens of a desired low f^(#)).
 22. A method offabricating a plurality of microlenses comprising: applying an adhesivehydrophobic layer to a substrate; lithographically patterning thehydrophobic layer into a plurality of areas; selectively etching thepatterned hydrophobic layer; dipping the substrate with its selectivelyetched patterned hydrophobic layer into a curable liquid monomersolution; and controllably withdrawing the substrate from the solutionso that, as the substrate is withdrawn, the liquid monomer solutiondrains from the hydrophobic areas of the substrate but remains on thehydrophilic areas, the solution forming in these hydrophilic areas capsunder the influence of surface tension; and curing the caps of curablemonomer present upon the substrate so as to make a plurality of solidpolymer microlenses.
 23. The method of fabricating a plurality ofmicrolenses according to claim 22 that, after the curing, furthercomprises: re-dipping the substrate with its plurality of polymermicrolenses into the liquid monomer solution so that additional monomersolution assembles on top of the existing cured microlenses;re-withdrawing the substrate from the solution; and re-curing thenewly-added curable monomer present upon the plurality of microlensesupon the substrate so as to make microlenses having decreased radii ofcurvature, and a corresponding reduction in f^(#).
 24. The method offabricating a plurality of microlenses according to claim 23 wherein there-dipping, the re-withdrawing and the re-curing are performedrepeatedly so as to produce microlenses of a desired low f^(#)).
 25. Themethod of fabricating a plurality of microlenses according to claim 22wherein the applying of the adhesive hydrophobic layer to the substrateis mechanical.
 26. The method of fabricating a plurality of microlensesaccording to claim 22 wherein the mechanical applying of the adhesivehydrophobic layer to the substrate is by use of a polishing cloth. 27.The method of fabricating a plurality of microlenses according to claim22 wherein the applying of the adhesive hydrophobic layer is to asubstrate drawn from the Si; Si; SiN, SiO₂; GaAs; InGaAs; and InP. 28.The method of fabricating a plurality of microlenses according to claim22 wherein the dipping of the substrate is into a UV-curable liquidmonomer solution; and wherein the curing of the spherical caps ofcurable monomer present upon the substrate is with UV light.
 29. Themethod of fabricating a plurality of microlenses according to claim 22wherein the dipping of the substrate is into a monomer solution rangingin viscosity from μ˜20 centipoise to μ˜2000 centipoise.
 30. The methodof fabricating a plurality of microlenses according to claim 22 whereinthe lithographic patterning of the hydrophobic layer into a plurality ofregularly geometrically sized and related areas is conducted so that theplurality of microlenses ultimately formed by the curing are in aregular array.
 31. The method of fabricating a plurality of microlensesaccording to claim 22 wherein the withdrawing of the substrate from themonomer solution is controlled in at least one of (i) monomer viscosity,(ii) monomer surface tension, (iii) substrate dipping angle, (iv) speedof substrate withdrawal, (v) fill factor of any array formed byproximate ones of the plurality of microlenses, and (vi) the number oftimes the dipping, the withdrawing and the curing are repetitivelyperformed, (vii) monomer solution density, and (viii) surface freeenergies of the hydrophobic and hydrophilic areas of the substrate. 32.The method of fabricating a plurality of microlenses according to claim31 wherein the withdrawing of the substrate from the monomer solution iscontrolled in all of (i) monomer viscosity, (ii) monomer surfacetension, (iii) substrate dipping angle, (iv) speed of substratewithdrawal, (v) fill factor of any array formed by proximate ones of theplurality of microlenses, and (vi) the number of times the dipping, thewithdrawing and the curing are repetitively performed.
 33. A microlens,part of a plurality of microlenses, fabricated by the method of claim31.
 34. The method according to claim 31 adapted and extended to thefabrication of a plurality of microlenses that are self-aligned to asmall light source including as appears at the ends of optical fibersand low-wavelength single-mode light output devices, the adapted andextended method wherein, after applying of the adhesive hydrophobiclayer to a substrate that is transparent, transpires another, second,applying of photoresist; and then the small light source is affixed headon to the substrate; and then light from the light source is used toexpose the photoresist substantially only where it is affixed to thesubstrate; and then the selectively etching serves to etch away thehydrophobic layer from the exposed region, followed by stripping theremaining photoresist, leaving a hydrophilic area in a hydrophobicbackground on the substrate in position opposite to light output fromthe affixed light source; so that then the dipping of the substrate withits selectively etched patterned hydrophobic layer and affixed lightsource into a curable monomer solution; followed by the controlledwithdrawing the substrate from the solution; followed by the curing ofthe monomer as is upon the withdrawn substrate into polymer; inaggregate serves to produce a microlens upon the substrate in a shape,and in a size, of light output from the light source, and in positionopposite the light source; wherein the produced microlens is useful toguide light emitted from the light source.
 35. The method of fabricatinga plurality of microlenses according to claim 22 wherein the withdrawingof the substrate from the monomer solution is controlled in at least oneof (i) monomer viscosity, (ii) monomer surface tension, (iii) substratedipping angle, (iv) speed of substrate withdrawal, (v) fill factor ofany array formed by proximate ones of the plurality of microlenses, and(vi) the number of times the dipping, the withdrawing and the curing arerepetitively performed, (vii) monomer solution density, and (viii)surface free energies of the hydrophobic and hydrophilic areas of thesubstrate.
 36. A small light source self-aligned to a microlens, andvice-versa, by the method of claim
 34. 37. A method of fabricating amicrolens precision sized and aligned and spatially positioned to asmall light source, the method comprising: affixing, and directing thelight output of, a small light source to a transparent spacer elementhaving a surface on which is present an adhesive hydrophobic layer and aphotoresist layer; patterning the surface of the spacer element byexposing the photoresist with, only at the light output of, the smalllight source, then etching away the hydrophobic layer at and from theexposed region, then stripping remaining photoresist so as to leave ahydrophilic domain in a hydrophobic background sized, shaped andjuxtaposed relative to the light output of the light source; and forminga polymer microlens upon the patterned surface of the spacer element byimmersing the surface-patterned spacer element in a curable liquidmonomer solution, then withdrawing the spacer element from solution soas to leave in the hydrophilic area of its patterned surface a sphericalcap of the monomer, then curing the spherical monomer cap to form apolymer microlens; wherein the microlens, located upon the surface ofthe spacer element in a shape, and in a size, of light output from thelight source, and in position juxtaposed to the light source, is usefulto guide light emitted from the light source into the affixedtransparent spacer element.
 38. The method of precision fabricating amicrolens according to claim 37 wherein the affixing of the small lightsource to the transparent spacer element is by transparent adhesive. 39.The method of precision fabricating a microlens according to claim 37wherein the affixing of the small light source is to a major surface ofa transparent spacer element in the shape of a rectilinear substrate.40. The method of precision fabricating a microlens according to claim37 wherein the exposing of the photoresist with light output of thesmall light source during the patterning of the surface of the spacerelement comprises: controlling at least one of (1) intensity, (2)duration and (3) numerical aperture of the small light source so as tocontrol size of an area of photoresist that is exposed, and subsequentlyetched; wherein the area of the microlens ultimately formed on thesurface of the spacer element is controllable.
 41. The method ofprecision fabricating a microlens according to claim 37 wherein theetching of the hydrophobic layer at and from the exposed region is by O₂plasma.
 42. The method of precision fabricating a microlens according toclaim 37, wherein the immersing the surface-patterned spacer element isinto a UV curable liquid monomer solution, and wherein the curing of thespherical monomer cap to form a polymer microlens is by UV light. 43.The method of precision fabricating a microlens according to claim 37wherein, in the forming of the polymer microlens upon thesurface-patterned spacer element, each of the immersing and thewithdrawing and the curing are repeated to form a polymer microlens witha decreased radius of curvature, and a corresponding reduction in f^(#).44. The method of precision fabricating a microlens according to claim37 performed in parallel on a multiplicity of small light sources. 45.The method of precision fabricating a microlens according to claim 37performed on an optical fiber.
 46. A microlens precision fabricated bythe method of claim
 37. 47. A small light source emitting light passingthrough a microlens that is precision-fabricated by the method of claim37.
 48. A method of fabricating a microlens upon the end of an opticalfiber, the method comprising: coating the end of an optical fiber firstwith a hydrophobic material and then with a photoresist; patterning thehydrophobic material upon the optical fiber end by exposing thephotoresist with light output from the optical fiber source, thenetching away the hydrophobic material at and from the exposed region,then stripping remaining photoresist so as to leave a hydrophilic domainsized and shaped relative to the light output of the optical fiber; andforming a polymer microlens upon the patterned optical fiber end byimmersing the patterned optical fiber end in a curable liquid monomersolution, then withdrawing the optical fiber end from the monomersolution so as to leave in the hydrophilic area of the optical fiber enda spherical cap of the monomer, then curing the spherical monomer cap toform a polymer microlens; wherein the microlens, located upon theoptical fiber end in a shape, and in a size of, light that is outputfrom the optical fiber, is useful to guide this light output from theoptical fiber.
 49. The method of fabricating a microlens upon the end ofan optical fiber according to claim 48 wherein the coating of the end ofthe optical fiber with the hydrophobic material is by a mechanicalprocess.
 50. The method of fabricating a microlens upon the end of anoptical fiber according to claim 48 wherein the coating of the end ofthe optical fiber with the photoresist is by process of dabbing.
 51. Themethod of precision fabricating a microlens according to claim 48performed in parallel on a multiplicity of optical fibers.
 52. Amicrolens precision fabricated upon the end of an optical fiber by themethod of claim
 48. 53. An optical fiber having an end upon which amicrolens is precision fabricated by the method of claim
 48. 54. Amethod of fabricating conductive polymer bump bonds self-aligned toregions upon a substrate comprising: applying a hydrophobic layer to aheterogeneous substrate consisting of a plurality of different materialsso that at least one material of the substrate where, and to which,electrical connection is desired to be made remains hydrophilic;followed by transferring a liquid conductive-material-precursor tohydrophilic areas of the substrate; followed by curing the liquidconductive-material-precursor which is upon at least one material of thesubstrate where, and to which, electrical connection is desired to bemade to form solid conductive polymer bump bonds; wherein the bump bondsare self-aligned to a material, and to regions, of the substrate where,and to which, electrical connection is desired to be made.
 55. Themethod according to claim 54 wherein the regions are contact pads; andwherein the material of the contact pad regions, which material remainshydrophilic, is metal.
 56. The method according to claim 54 wherein thetransferring of the liquid conductive-material-precursor to hydrophilicareas of the substrate comprises: condensing a liquidconductive-material-precursor on the hydrophilic areas of the substrate.57. The method according to claim 54 wherein the transferring of theliquid conductive-material-precursor to hydrophilic areas of thesubstrate comprises: immersing the substrate in a liquidconductive-material-precursor solution; and then withdrawing thesubstrate from the solution so as to leave in the hydrophilic areas ofthe substrate caps of the liquid conductive-material-precursor.
 58. Amethod of fabricating conductive polymer bump bonds self-aligned toregions upon a substrate comprising: patterning a heterogeneoussubstrate consisting of contact pad regions of one material and other,non-contact-pad regions not of the contact region material, so that ahydrophobic layer overlies all regions of the substrate except thecontact pad regions, which contact pad regions remain hydrophilic;transferring a liquid conductive polymer precursor onto the hydrophiliccontact pad regions of the substrate; and solidifying the liquidconductive polymer precursor that is upon the contact pad regions of thesubstrate to form conductive polymer bump bonds; wherein the conductivepolymer bump bonds are, by consequence of the manner of their creation,aligned to the contact pads of the substrate.
 59. The method accordingto claim 58 wherein the transferring of the liquid conductive polymerprecursor to hydrophilic contact pad regions of the substrate comprises:condensing the liquid conductive polymer precursor on the hydrophilicareas of the substrate.
 60. The method according to claim 58 wherein thetransferring of the liquid conductive polymer precursor to hydrophiliccontact pad regions of the substrate comprises: immersing the substratein a solution of the liquid conductive polymer precursor; and thenwithdrawing the substrate from the solution so as to leave in thehydrophilic areas of the substrate caps of the liquid conductive polymerprecursor.
 61. The method according to claim 58 wherein the solidifyingcomprises: curing the liquid polymer precursor.
 62. The method accordingto claim 58 wherein the solidifying comprises: permitting solvent toevaporate from the liquid polymer precursor so as to leave the solidconductive polymer bump bonds.
 63. A method of fabricating conductivebumps between mutually perpendicular surfaces, and self-aligned toregions upon these surfaces comprising: applying a hydrophobic layer totwo surfaces consisting of a plurality of different materials so that atleast one material of each surface where, and to which, electricalconnection is desired to be made remains hydrophilic; followed bytransferring a liquid that is a conductive-material-precursor tohydrophilic areas of the surfaces; followed by attaching the twosurfaces together in a mutually perpendicular fashion, such that theliquid conductive-material-precursor on the hydrophilic areas of onesurface makes contact with the liquid conductive-material-precursor onthe second surface at precise locations curing the liquidconductive-material-precursor to form solid conductive bonds between thetwo mutually perpendicular surfaces; wherein solid conductive bonds areformed between the two surfaces that are self-aligned to a material oneach surface where, and to which, electrical connection is desired to bemade.
 64. The method according to claim 63 wherein the regions arecontact pads; and wherein the material of the contact pad regions, whichmaterial remains hydrophilic, is metal.
 65. The method according toclaim 63 wherein the transferring of the liquidconductive-material-precursor to hydrophilic areas of the substratescomprises: condensing a liquid conductive-material-precursor on thehydrophilic areas of the substrate.
 66. The method according to claim 63wherein the transferring of the liquid conductive-material-precursor tohydrophilic areas of the substrates comprises: immersing the substratein a liquid conductive-material-precursor solution; and then withdrawingthe substrate from the solution so as to leave in the hydrophilic areasof the substrate caps of the liquid conductive-material -precursor. 67.A method of fabricating conductive bonds between mutually perpendicularsurfaces, and self-aligned to regions upon these surfaces comprising:patterning two heterogeneous substrates consisting of contact padregions of one material and other, non-contact-pad regions not of thecontact region material, so that a hydrophobic layer overlies allregions of the substrates except the contact pad regions, which contactpad regions remain hydrophilic; transferring a liquidconductive-material-precursor onto the hydrophilic contact pad regionsof both substrates; and attaching the two substrates together in amutually perpendicular fashion, such that the liquidconductive-material-precursor on the hydrophilic areas of one substratemakes contact with the liquid conductive-material-precursor on thesecond substrate at precise locations; and solidifying the liquidconductive-material-precursor that is upon the contact pad regions ofthe substrate to form conductive bonds; wherein the bonds are, byconsequence of the manner of their creation, aligned to the contact padsof the substrate, and connect the two mutually perpendicular substrateselectrically.
 68. The method according to claim 67 wherein thetransferring of the liquid conductive-material-precursor to hydrophiliccontact pad regions of the substrate comprises: condensing the liquidconductive-material-precursor on the hydrophilic areas of the substrate.69. The method according to claim 67 wherein the transferring of theliquid conductive-polymer-precursor to hydrophilic contact pad regionsof the substrates comprises: immersing the substrates in a solution ofthe liquid conductive polymer precursor; and then withdrawing thesubstrates from the solution so as to leave in the hydrophilic areas ofthe substrate caps of the liquid conductive polymer precursor, thevolume of which may be controlled by adjusting (i) liquid viscosity,(ii) liquid surface tension, (iii) liquid density, (iv) thesurface-free-energies of the hydrophilic and hydrophobic areas of thesubstrate (v) the angle of substrate withdrawal, (vi) the speed of thesubstrate withdrawal, (vii) the proximity of hydrophilic areas to eachother, and (viii) the number of times the dip-coating process isperformed.
 70. The method according to claim 67 wherein the solidifyingcomprises: curing the liquid polymer precursor.
 71. The method accordingto claim 67 wherein the solidifying comprises: permitting solvent toevaporate from the liquid polymer precursor so as to leave the solidconductive polymer bonds.
 72. A method of fabricating electricalcontacts between substrates comprising: patterning a hydrophobic layeron each of two heterogeneous substrates such that at least onecorresponding domain on each substrate remains hydrophilic; then, ineither order, transferring a liquid conductive-polymer-precursor to thehydrophilic areas of both substrates, and bringing the substratestogether so that one or more corresponding domains on each substrate areproximate; then curing of the liquid conductive-polymer-precursor so asto bond the two substrates together with electrical connection betweencorresponding domains on each substrate.
 73. The method according toclaim 72 wherein the substrates are mutually perpendicular.
 74. Themethod according to claim 72, that, after the bringing, furthercomprises: physically attaching the two substrates together.
 75. Themethod according to claim 74 wherein the physically attaching comprises:adhering with epoxy.